100+ LCM and HCF Questions for IBPS PO, SO, Clerk Pdf - 1

Question: 1

LCM and HCF of two numbers are 48 and 8 respectively. If one of the numbers is 16, the second number is

(A) 12

(B) 18

(C) 24

(D) 36

Ans: C

Second number = $${LCM × HCF} / {First number}$$ = $${48 × 8} / {16}$$ = 24.

Question: 2

The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is

(A) 12

(B) 16

(C) 24

(D) 48

Ans D

Let the numbers be 3x and 4x.

Then, their H.C.F. = x.

So, x = 4.

So, the numbers are 12 and 16.

L.C.M. of 12 and 16 = 48.

Question: 3

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

Ans: C

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

∴ Larger number = (23 × 14) = 322.

Question: 4

Four metal rods of lengths 78 cm, 104 cm, 117 cm and 169 cm are to be cut into parts of equal length. Each part must be as long as possible. What is the maximum number of pieces that can be cut?

(A) 27

(B) 36

(C) 43

(D) 480

Ans: B

Maximum length of each part

= H.C.F. of 78 cm, 104 cm, 117 cm, 169 cm = 13 cm.

∴ Number of pieces = $$({78 + 104 + 117 + 169} / {13})$$ = $${468}/{13}$$ = 36.

Question: 5

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

(A) 504

(B) 536

(C) 544

(D) 548

Ans: D

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

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