What is the least number which, when doubled, is exactly divisible by 12, 18, 21, and 30?

Concept / Approach

• Let the required number be n. Then 2n must be a common multiple of 12, 18, 21, and 30.
• The least such multiple is the LCM; hence take n = LCM/2.

Step-by-step calculationLCM(12,18,21,30) = 12602n = 1260 ⇒ n = 1260/2 = 630

Verification2×630 = 1260 which is divisible by 12, 18, 21, and 30.

Final Answer630