Find the L.C.M. of 24, 36, and 40.

Given data

• Numbers: 24, 36, 40.

Concept / Approach

• Use prime powers: take the highest power of each prime appearing in any number.

Prime factorization

24 = 2^3 × 336 = 2^2 × 3^240 = 2^3 × 5LCM = 2^3 × 3^2 × 5 = 8 × 9 × 5 = 360.

Verification

360 ÷ 24 = 15; 360 ÷ 36 = 10; 360 ÷ 40 = 9 ⇒ all integers.

Final Answer

L.C.M. = 360.