Two numbers are in the ratio 2:3 and their L.C.M. is 48. Find the sum of the numbers.

Given data

• Numbers in ratio 2:3 ⇒ let them be 2k and 3k.
• LCM(2k, 3k) = 48.

Concept / Approach

• For coprime 2 and 3, LCM(2k, 3k) = 6k.
• Solve for k, then compute the numbers and their sum.

Step-by-step calculation

6k = 48 ⇒ k = 8.Numbers: 2k = 16 and 3k = 24.Sum = 16 + 24 = 40.

Verification

LCM(16, 24) = 48 ✔

Common pitfalls

• Using G.C.D. instead of L.C.M. relation; or forgetting that 2 and 3 are coprime.

Final Answer

Sum of the numbers = 40.