Which is the smallest number which when divided by 8 9 10 15 20 gives a remainder of 5 every time? 2021

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Solutions for Class 7 Math Chapter 3 Hcf And Lcm are provided here with simple step-by-step explanations. These solutions for Hcf And Lcm are extremely popular among Class 7 students for Math Hcf And Lcm Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Mathematics Solutions Book of Class 7 Math Chapter 3 are provided here for you for không lấy phí. You will also love the ad-không lấy phí experience on Meritnation’s Mathematics Solutions

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  • What is the smallest square number divisible by 8 9 and 10?

  • What is the smallest number divisible by 10 15 and 20?

  • Which number amongst 20 3 418 and 8 is the smallest?

  • Which of the following is the least number which will leave the remainder 5 when divisible by 8 12 16 20?


Page No 15:



Question 1:


Which number is neither a prime number nor a composite number?



Answer:


1 is neither a prime number nor a composite number.


Page No 15:



Question 2:


Which of the following are pairs of co-primes?
(i) 8,

14
(ii) 4, 5
(iii) 17, 19
(iv) 27, 15
 



Answer:


Two numbers which have only 1 as a common factor are said to be co-prime or relatively prime or mutually prime numbers.
We can write 17 as 17 × 1 and 19 as 17 × 1.
Hence, 17 and 19 is a pair of co-prime numbers.


Page No 15:



Question 3:


List the prime numbers from 25 to 100 and say how many they are.



Answer:


There are a total of 16 prime numbers between 25 and 100 which are 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.


Page No 15:



Question 4:


Write all the twin prime numbers from 51 to 100.



Answer:


If the difference between two co-prime numbers is 2, the numbers are said to be twin prime numbers.
Hence, the twin

prime numbers between 51 and 100 are 59 and 61, 71 and 73.


Page No 15:



Question 5:


Write 5 pairs of twin prime numbers from 1 to 50.



Answer:


If the difference between two co-prime numbers is 2 then, the numbers are said to be twin prime numbers.
Hence, the twin prime numbers from 1 to 50 are (2,3), (5,7), (11,12), (17,19) and (29,30).


Page No 15:



Question 6:


Which are the even prime

numbers?



Answer:


There is only even prime number which is 2.


Page No 17:



Question 1:


Factorise the following numbers into primes.
(i)    32
(ii)   57
(iii)  23
(iv)  150
(v)   216
(vi)  208
(vii) 765
(viii) 342
(ix)   377
(x)    559



Answer:


(i)
32 = 2 × 16
= 2 ×

2 × 8
= 2 × 2 × 2 × 4
​= 2 × 2 × 2 × 2 × 2
(ii)
57 = 3 × 19
(iii)
23 = 23 × 1
(iv)
150 = 2 × 75
= 2 × 3 × 25
​= 2 × 3 × 5 × 5
(v)
216 =  2 × 108
 =  2 × 2 × 54
 =  2 × 2 × 2 × 27
 =  2 × 2 × 2 × 3 × 9
 =  2 × 2 × 2 × 3 × 3 × 3
(vi)
208 = 2 × 104
= 2 × 2 × 52
= 2 × 2 × 2 ×

26
= 2 × 2 × 2 × 2 × 13
(vii)
765 = 3 × 255
= 3 × 3 × 85
= 3 × 3 × 5 × 17
(viii)
342 = 2 × 171
= 2 × 3 × 57
= 2 × 3 × 3 × 19
(ix)
377 = 13 × 29
(x)
559 = 13 × 43


Page No 19:



Question 1:


Find the HCF.
(i)     25, 40
(ii)    56, 32
(iii)   40, 60, 75
(iv)   16, 27
(v)    18,

32, 48
(vi)   105, 154
(vii)  42, 45, 48
(viii) 57, 75, 102
(ix)   56, 57
(x)    777, 315, 588



Answer:



(i)
 


Which is the smallest number which when divided by 8 9 10 15 20 gives a remainder of 5 every time?

HCF = 5




(ii)
 


Which is the smallest number which when divided by 8 9 10 15 20 gives a remainder of 5 every time?

HCF = 2 × 2 × 2= 8


(iii)


Which is the smallest number which when divided by 8 9 10 15 20 gives a remainder of 5 every time?

HCF = 5


(iv)
 


Which is the smallest number which when divided by 8 9 10 15 20 gives a remainder of 5 every time?

HCF = 1


(v)
 


Which is the smallest number which when divided by 8 9 10 15 20 gives a remainder of 5 every time?

HCF = 2


(vi)
 


Which is the smallest number which when divided by 8 9 10 15 20 gives a remainder of 5 every time?

HCF = 7


(vii)
 


Which is the smallest number which when divided by 8 9 10 15 20 gives a remainder of 5 every time?

HCF = 3


(viii)
 


Which is the smallest number which when divided by 8 9 10 15 20 gives a remainder of 5 every time?

HCF = 3


(ix)
 


Which is the smallest number which when divided by 8 9 10 15 20 gives a remainder of 5 every time?

HCF = 1


(x)
 


Which is the smallest number which when divided by 8 9 10 15 20 gives a remainder of 5 every time?

HCF = 3 × 7 = 21


Page No 19:



Question 2:



Find the HCF by the division method and reduce to the simplest form.


(i) 275525


(ii) 76133


(iii) 16169



Answer:



(i) 


Which is the smallest number which when divided by 8 9 10 15 20 gives a remainder of 5 every time?

HCF = 25
 ∴275525=275÷25525÷25=1121


(ii)


Which is the smallest number which when divided by 8 9 10 15 20 gives a remainder of 5 every time?

HCF = 19
 ∴76133=76÷19133÷19=47


(iii) 


Which is the smallest number which when divided by 8 9 10 15 20 gives a remainder of 5 every time?

HCF = 23
∴16169=161÷2369÷23=

73


Page No 21:



Question 1:


Find the LCF.
(i)     12, 15
(ii)    6, 8, 10
(iii)   18, 32
(iv)   10, 15, 20
(v)    45, 86
(vi)   15, 30, 90
(vii)  105, 195
(viii) 12, 15, 45
(ix)   63, 81
(x)    18, 36, 27



Answer:



(i)


Which is the smallest number which when divided by 8 9 10 15 20 gives a remainder of 5 every time?

LCM = 3 × 5 × 4 = 60


(ii)


Which is the smallest number which when divided by 8 9 10 15 20 gives a remainder of 5 every time?

LCM = 2 × 3 × 4 × 5​ = 120


(iii)


Which is the smallest number which when divided by 8 9 10 15 20 gives a remainder of 5 every time?

LCM = 2 × 9 × 16 ​= 288


(iv)


Which is the smallest number which when divided by 8 9 10 15 20 gives a remainder of 5 every time?

LCM = 2 × 2 × 3 × 5 = 60


(v)


Which is the smallest number which when divided by 8 9 10 15 20 gives a remainder of 5 every time?

LCM = 45 × 86 = 3870


(vi)


Which is the smallest number which when divided by 8 9 10 15 20 gives a remainder of 5 every time?

LCM = 2 × 3 × 3 × 5 = 90


(vii)


Which is the smallest number which when divided by 8 9 10 15 20 gives a remainder of 5 every time?

LCM = 3 × 5 × 7 × 13 = 1365


(viii)


Which is the smallest number which when divided by 8 9 10 15 20 gives a remainder of 5 every time?

LCM = 2 × 2 × 3 × 3 × 5 = 180




(ix)


Which is the smallest number which when divided by 8 9 10 15 20 gives a remainder of 5 every time?

LCM = 3 × 3 × 3 × 3 × 5 = 567


(x)


Which is the smallest number which when divided by 8 9 10 15 20 gives a remainder of 5 every time?

​LCM = 2 × 2 × 3 × 3 × 3 = 108


Page No

21:



Question 2:


Find the HCF and LCM of the numbers given below. Verify that their product is equal to the product of the given numbers.
(i) 32, 37
(ii) 46, 51
(iii) 15, 60
(iv) 18, 63
(v) 78, 104



Answer:



(i) 


Which is the smallest number which when divided by 8 9 10 15 20 gives a remainder of 5 every time?

HCF = 1

LCM = 32 × 37 = 1184
Product of two numbers = 32 × 37 = 1184
Product of HCF and LCM = 1 × 1184 = 1184


(ii) 


Which is the smallest number which when divided by 8 9 10 15 20 gives a remainder of 5 every time?

HCF = 1
LCM = 46 × 51 = 2346
Product of two numbers = 46 × 51= 2346
Product of HCF and LCM  = 1 × 2346 = 2346


(iii) 


Which is the smallest number which when divided by 8 9 10 15 20 gives a remainder of 5 every time?

HCF = 3 × 5 = 15
LCM = 3 × 5 × 4 = 60
Product of two numbers = 15 × 60 = 900
Product of HCF and LCM = 15 × 60 = 900


(iv) 


Which is the smallest number which when divided by 8 9 10 15 20 gives a remainder of 5 every time?

HCF = 3 × 3 = 9
LCM = 3 × 3 × 2 × 7 = 126
Product of two numbers = 18 × 63 = 1134
Product of HCF and LCM = 9 × 126 = 1134
(v) 


Which is the smallest number which when divided by 8 9 10 15 20 gives a remainder of 5 every time?

HCF = 2 × 13 = 26
LCM = 2 × 13 × 3 × 4 = 312
Product of two numbers =  78 × 104 = 8112
Product of HCF and LCM  = 26 × 312 = 8112


Page No 23:



Question 1:



Choose the right option.
(i) The HCF of 120 and 150 is

………………. .
(1) 30
(2) 45
(3) 20
(4) 120


(ii) The HCF of this pair of numbers is not 1.
(1) 13, 17
(2) 29, 20
(3) 40, 20
(4) 14, 15



Answer:


(i)
 


Which is the smallest number which when divided by 8 9 10 15 20 gives a remainder of 5 every time?

HCF = 2 × 3 × 5 = 30
Hence, the correct answer is

option (1).
(ii)
40 = 2 × 2 × 2 × 5
20 = 2 × 2 × 5
The HCF of 20 and 40 is 2 × 2 × 5 or 20.
Hence, the correct answer is option (3).


Page No 23:



Question 2:


Find the HCF and LCM.
(i) 14, 28
(ii) 32, 16
(iii) 17, 102, 170
(iv) 23, 69
(v) 21, 49, 84



Answer:



(i) 


Which is the smallest number which when divided by 8 9 10 15 20 gives a remainder of 5 every time?

HCF = 2 × ​7 = 14
LCM = 2 × ​7 × 2 = 28


(ii) 


Which is the smallest number which when divided by 8 9 10 15 20 gives a remainder of 5 every time?

HCF = 2 × ​2 × ​2 × 2 = 16
LCM = 2 × ​2 × ​2 × 2 × 2 = 32


(iii) 



Which is the smallest number which when divided by 8 9 10 15 20 gives a remainder of 5 every time?

HCF = 17
LCM = ​17 × ​2 × ​3 × 5 = 510


(iv) 


Which is the smallest number which when divided by 8 9 10 15 20 gives a remainder of 5 every time?

HCF = 23
LCM = ​23 × 3 = 69


(v) 


Which is the smallest number which when divided by 8 9 10 15 20 gives a remainder of 5 every time?

HCF = 7
LCM = ​3 × ​4 × ​7 × 7 = 588


Page No 23:



Question 3:


Find the LCM.
(i) 36, 42
(ii) 15, 25, 30
(iii) 18, 42, 48
(iv) 4, 12, 20
(v) 24, 40, 80, 120



Answer:



(i) 


Which is the smallest number which when divided by 8 9 10 15 20 gives a remainder of 5 every time?

LCM = 2 × ​2 × 3 × 3 × 7 = 252


(ii) 


Which is the smallest number which when divided by 8 9 10 15 20 gives a remainder of 5 every time?

LCM = 2 × ​3 × 5 × 5 = 150




(iii) 


Which is the smallest number which when divided by 8 9 10 15 20 gives a remainder of 5 every time?

LCM = 2 × ​2 × 2 × 2 × 3 × 3 × 7 = 1008


(iv) 


Which is the smallest number which when divided by 8 9 10 15 20 gives a remainder of 5 every time?

LCM = 2 × ​2 × 3 × 5 = 60


(v) 


Which is the smallest number which when divided by 8 9 10 15 20 gives a remainder of 5 every time?

LCM = 2 × ​2 × 2 × 2 × 3 × 5 = 240


Page No 23:



Question 4:


Find the smallest number which when divided by 8, 9, 10, 15, 20 gives a remainder of 5 every time.



Answer:


LCM of  8, 9, 10, 15, 20 is given

by


Which is the smallest number which when divided by 8 9 10 15 20 gives a remainder of 5 every time?

LCM = 2 × 2 × 2 × 3 × 3 × 5 = 360
Hence, 365 is the smallest number which when divided by 8, 9, 10, 15, 20 gives a remainder of 5 every time.


Page No 23:



Question 5:


Reduce the fractions

348319 , 221247 , 437551 to the lowest terms.



Answer:


348319=348÷29319÷29

=1211
221247=221÷13247÷13=1719
437551=

437÷19551÷19=2329 


Page No 23:



Question 6:


The LCM and HCF of two numbers are 432 and 72 respectively. If one of the numbers is 216, what is the other ?



Answer:


Let the other number be x.
Now, HCF × LCM = Product of

two numbers
⇒ 72 × 432 = x × 216
⇒x=72×432216
= 144
​Hence, the other number is 144.


Page No 23:



Question 7:


The product of two two-digit numbers is 765 and their HCF is 3. What is their LCM?



Answer:


HCF × LCM = Product of two numbers

⇒ 3 × LCM = 765
⇒LCM=7653
= 255
Hence, the LCM of the two numbers is 255.


Page No 23:



Question 8:


A trader has three bundles of string 392 m, 308 m and 490 m long. What is the great est length of string that the bundles can be cut up into without any left over string?



Answer:


The greatest

length of string that the bundles can be cut up into without any left over string is given by the HCF of 392, 308 and 490.


Which is the smallest number which when divided by 8 9 10 15 20 gives a remainder of 5 every time?

HCF = 2 × 7 = 14 
Hence, the greatest length of string that the bundles can be cut up into without any left over string is 14 m.


Page No 23:



Question 9:


Which two consecutive even numbers have an LCM of 180?



Answer:


Let us suppose the two consecutive even numbers be 2x and 2x + 2.
Now, product of two numbers = HCF × LCM
⇒ (2x)(2x + 2) = 2 × 180            (Hồ Chí Minh of two even number is 2)
⇒ (x)(2x + 2) = 180  
⇒ 2×2 + 2x =

180   
⇒ 2×2 + 2x − 180 = 0
⇒ x2 + x − 90 = 0
⇒ (x − 9)(x + 10) = 0
⇒ x − 9 = 0 or x + 10 = 0
⇒ x = 9 or x =  −10 (Neglecting)
Hence, the two consecutive even numbers are18 and 20.



View NCERT Solutions for all chapters of Class 7




What is the smallest square number divisible by 8 9 and 10?


Hence, 3600 is the smallest square number divisible by each one of the numbers 8 , 9 and 10.

What is the smallest number divisible by 10 15 and 20?


LCM of 10, 15, and 20 by Listing Multiples

Step 3: The smallest common multiple of 10, 15, and 20 is 60.

Which number amongst 20 3 418 and 8 is the smallest?


So, the only option left which can be the smallest number is 321. Hence, option 2 is correct. The Union Public Service Commission (UPSC) has released the admit card for UPSC IAS main examination. The exam is scheduled to be held on the 16th, 17th, 18th, 24th, and 25th of September 2022.

Which of the following is the least number which will leave the remainder 5 when divisible by 8 12 16 20?


240 is the smallest number when divided by 8, 12, 16 and 20 always leaves remainder equal to zero.

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