100+ HCF and LCM Questions and Answers for Competitive Exams - 1

Question: 1

Two numbers are in the ratio of 15 : 11. If their HCF is 13, then the numbers are

(A) 15, 11

(B) 75, 55

(C) 195, 143

(D) 199, 147

Ans: C

Let the required numbers be 15a and 11a. Then

H.C.F. = x, so x = 13.

∴ Numbers are (15 × 13 and 11 × 13) i.e. 195, 143.

Question: 2

The HCF and LCM of two numbers are 50 and 250 respectively. If the first number is divided by 2, the quotient is 50. The second number is

(A) 50

(B) 75

(C) 100

(D) 125

Ans: D

First number = (50 x 2) = 100.

Second number = $$(50 × {250} /{100})$$ = 125.

Question: 3

The smallest number which when increased by 5 is divisible by each one of 24, 32, 36 and 54 is

(A) 859

(B) 869

(C) 4320

(D) 4520

Ans: A

Required number = (LCM of 24, 32, 36, 54) – 5 = 864 – 5 = 859.

Question: 4

An electronic device makes a beep after every 60 sec. Another device makes a beep after every 62 sec. They beeped together at 10 A.M. The time when they will next make a beep together at the earliest is

(A) 10.30 A.M.

(B) 10.31 A.M.

(C) 10.59 A.M.

(D) 11 A.M.

Ans: B

LCM of 60 and 62 seconds = 1860 sec = 31 min.

∴ They will beep together at 10.31 A.M.

Question: 5

Which of the following is a pair of co-prime?

(A) (16, 62)

(B) (18, 25)

(C) (21, 35)

(D) (23, 92)

Ans: B

H.C.F. of 18 and 25 is 1. So they are co-primes.

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