HCF and LCM Questions

HCF and LCM Questions

09 May 2023


While Preparing for Quantitative aptitude tests, questions on Number system- HCF and LCM are asked frequently.


Top 10 HCF and LCM Questions

Q1) Two numbers are in the ratio 2 : 3. If their L.C.M. is 48. what is sum of the numbers?

A) 64

B) 42

C) 28

D) 40

Solution :


Q2) What is the greatest number of four digits which is divisible by 15, 25, 40 and 75 ?

A) 9200

B) 9600

C) 9800

D) 9400

Solution :


Q3) Three numbers are in the ratio of 2 : 3 : 4 and their L.C.M. is 240. Their H.C.F. is:???????

A) 40

B) 20

C) 10

D) 30

Solution :


Q4) What is the lowest common multiple of 12, 36 and 20?

A) 120

B) 160

C) 220

D) 1

Solution :


Q5) H.C.F. of 513, 1134 and 1215 is _____________ 

A) 18

B) 27

C) 33

D) 36

Solution : 

We know different methods to calculate H.C.F. 

Finding H.C.F. by division method: 



H.C.F. of 513, 1134 and 1215 = 3 × 3 × 3 = 27. 

Q6) The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively, is: 

A) 127

B) 305

C) 235

D) 123

Solution :

Required number = H.C.F. of (1657 - 6) and (2037 - 5) 

= H.C.F. of 1651 and 2032 = 127. 

Q7) The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is: 

A) 276

B) 299

C) 322

D) 345

Solution :

Clearly, the numbers are (23 x 13) and (23 x 14). 

Larger number = (23 x 14) = 322. 

Q8) HCF of 3/16, 5/12, 7/8 is: 

A) 2/47

B) 3/47 

C) 1/48 

D) 5/48 

Solution :

HCF of numerators = 1 

LCM of denominators = 48 

=> 1/48 

Q9) The least number, which when divided by 12, 15, 20 and 54 leaves in each case a remainder of 8 is: 

A) 544

B) 548

C) 504

D) 536

Solution :

Required number = (L.C.M. of 12, 15, 20, 54) + 8 = 540 + 8 = 548.

Q10) Find the lowest common multiple of 24, 36 and 40. 

A) 120

B) 240

C) 360

D) 480

Solution :

 

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