What is the least number which when doubled will be exactly divisible by…

Answer: 1386

We need the smallest integer x such that 2x is exactly divisible by 12, 14, 18 and 22.

• Find prime factorizations: 12 = 2^2 × 3, 14 = 2 × 7, 18 = 2 × 3^2, 22 = 2 × 11.

• Take highest powers of each prime: 2^2, 3^2, 7^1, 11^1. So LCM = 2^2 × 3^2 × 7 × 11 = 4 × 9 × 7 × 11 = 2772.

• Because 2x must equal the LCM, set 2x = 2772. Thus x = 2772 ÷ 2 = 1386.

• Check: 2 × 1386 = 2772, which is divisible by 12, 14, 18 and 22. Therefore the least such number is 1386.