Top 100+ H.C.F and L.C.M Problems with Solutions Pdf - 2

Question: 6

The H.C.F. of two numbers is 8. Which one of the following can never be their L.C.M.?

(A) 24

(B) 48

(D) 60

Ans: D

H.C.F. of two numbers divides their L.C.M. exactly. Clearly, 8 is not a factor of 60.

Question: 7

Find the highest common factor of 36 and 84.

(A) 4

(B) 6

(D) 12

Ans: D

36 = 2² × 3²; 84 = 2² × 3 × 7

∴ H.C.F. = 2² × 3 = 12.

Question: 8

252 can be expressed as a product of primes as

(A) 2 x 2 x 2 x 3 x 7

(B) 2 x 2 x 3 x 3 x 7

(D) 3 x 3 x 3 x 3 x 7

Ans: B

Clearly, 252 = 2 x 2 x 3 x 3 x 7.

Question: 9

About the number of pairs which have 16 as their HCF and 136 as their LCM, we can definitely say that

(A) Only one such pair exists

(B) No such pair exists

(D) Many such pairs exist

Ans: B

HCF of two numbers divides their LCM exactly.

Since 16 is not a factor of 136, it follows that there does not exist any pair of numbers with HCF 16 and LCM 136.

Question: 10

The H.C.F. of 0.54, 1.8 and 7.2 is

(A) 0.18

(B) 0.018

(D) 18

Ans: A

Given numbers are 0.54, 1.80 and 7.20.

H.C.F. of 54, 180 and 720 is 18.

∴ H.C.F. of given numbers = 0.18

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