Question

L.C.M. of two numbers is 12 time their H.C.F. The sum of H.C.F. and L.C.M. is 403. If one of the numbers is 124, then find the other number.
1. 112
2. 76
3. 64
4. 93

Answer 1

Correct Answer - Option 4 : 93

Given:

L.C.M. of two numbers is 12 time their H.C.F. The sum of H.C.F. and L.C.M. is 403.

One number is 124.

Concept Used:

LCM × HCF of two numbers = Product of those two numbers

Calculation:

Let, the HCF of two number be x

⇒ LCM of those two number is 12x

Accordingly,

x + 12x = 403

⇒ 13x = 403

⇒ x = 31

HCF of those two number is 31 and LCM = 31 × 12

Let, the other number be y

Now, LCM × HCF = Product of two numbers

⇒ 31 × 31 × 12 = 124 × y

⇒ y = 93

∴ The other number is 93.