Find the smallest 4 digit number which is divisible by 18, 24, 32?

Key idea: find the least common multiple (LCM) of the three numbers, then find the smallest 4-digit multiple of that LCM.

Prime factorization: 18 = 2 × 3², 24 = 2³ × 3, 32 = 2⁵.

LCM = 2⁵ × 3² = 32 × 9 = 288.

Smallest 4-digit multiple: compute ceil(1000 ÷ 288) = 4, so 288 × 4 = 1152.

• 1152 ÷ 18 = 64

• 1152 ÷ 24 = 48

• 1152 ÷ 32 = 36

Answer: 1152