Problems on H.C.F and L.C.M

Question: The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater number is:

[A].

101

[B].

107

[C].

111

[D].

185

Answer: Option C

Explanation:

Let the numbers be 37a and 37b.

Then, 37a x 37b = 4107

ab = 3.

Now, co-primes with product 3 are (1, 3).

So, the required numbers are (37 x 1, 37 x 3) i.e., (37, 111).

Greater number = 111.

Question:
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

Answer: Option D

Explanation:

Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 4.

So, the numbers 12 and 16.

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

Question:
The G.C.D. of 1.08, 0.36 and 0.9 is:

[A].

0.03

[B].

0.9

[C].

0.18

[D].

0.108

Answer: Option C

Explanation:

Given numbers are 1.08, 0.36 and 0.90.   H.C.F. of 108, 36 and 90 is 18,

H.C.F. of given numbers = 0.18.

Question:
252 can be expressed as a product of primes as:

[A].

2 x 2 x 3 x 3 x 7

[B].

2 x 2 x 2 x 3 x 7

[C].

3 x 3 x 3 x 3 x 7

[D].

2 x 3 x 3 x 3 x 7

Answer: Option A

Explanation:

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