Question

The L.C.M of two numbers is 99 times of H.C.F of the same numbers. Sum of the L.C.M and H.C.F is 700. If one of the numbers is 63, then the other number is:
1. 77
2. 49
3. 84
4. 70

Answer 1

Correct Answer - Option 1 : 77

Given:

L.C.M = 99 × H.C.F

L.C.M + H.C.F = 700

One of the number = 63

Formula used:

The Product of H.C.F and L.C.M of any two numbers is equal to the product of that numbers.

Calculation:

Let, H.C.F of the given numbers = X, then L.C.M = 99 × X = 99X

⇒ 99X + X = 700 (Given)

⇒ 100X = 700

⇒ X = 700/100 = 7

⇒ H.C.F = 7 and L.C.M = 99 × 7 = 693

Let, other number = n

Using formula,

⇒ 7 × 693 = 63 × n

⇒ n = (7 × 693)/63 = 7× 11 = 77

∴ Other number = 77