Question

The ratio of the ages of 4 friends A, B, C and D is 2 ∶ 3 ∶ 4 ∶ 5 and their HCF is 15. Find the LCM of the ages of all 4 friends.
1. 800
2. 500
3. 900
4. 700

Answer 1

Correct Answer - Option 3 : 900

Given∶

Ratio of the ages = 2 ∶ 3 ∶ 4 ∶ 5

Formula Used∶

Concept of HCF and LCM

Concept of Ratio

Calculation∶

Given ratio = 2 ∶ 3 ∶ 4 ∶ 5

Let the ages be 2x, 3x, 4x and 5x respectively.

∴ HCF = x = 15

So, the ages be, A’s age = 2 × 15 = 30 years

B’s age = 3 × 15 = 45 years

C’s age = 4 × 15 = 60 years

D’s age = 5 × 15 = 75 years

Now, LCM of 30, 45, 60, 75 = 2²× 3²× 5² = 900

∴ 900 is the LCM of the ages of A, B, C and D.