What is the smallest common multiple of the numbers 24, 36, and 40?

Explanation

To find the least common multiple (LCM) of 24, 36, and 40, we perform prime factorization and divide stepwise: Divide all numbers by 2: 24 ÷ 2 = 12, 36 ÷ 2 = 18, 40 ÷ 2 = 20 Divide again by 2: 12 ÷ 2 = 6, 18 ÷ 2 = 9, 20 ÷ 2 = 10 Divide once more by 2: 6 ÷ 2 = 3, 9 ÷ 1 = 9, 10 ÷ 2 = 5 Divide by 3: 3 ÷ 3 = 1, 9 ÷ 3 = 3, 5 ÷ 1 = 5 Divide by 3 again: 1 ÷ 1 = 1, 3 ÷ 3 = 1, 5 ÷ 1 = 5 Divide by 5: 1 ÷ 1 = 1, 1 ÷ 1 = 1, 5 ÷ 5 = 1 Multiplying all prime factors used: 2 × 2 × 2 × 3 × 3 × 5 = 360. Thus, the LCM of 24, 36, and 40 is 360.