Final answer:
The least common multiple of 30 and 24 is found by breaking down each number into its prime factors and then taking the highest power of each prime. By multiplying these together, we find that the LCM is 120.
Step-by-step explanation:
To find the least common multiple (LCM) of 30 and 24, we should first break each number down into its prime factors. The number 30 can be expressed as 2 × 3 × 5, and 24 can be expressed as 23 × 3. To determine the LCM, we take the highest power of each prime that appears in the factorization of either number. In this case, we have 23 (which is 8), 3, and 5.
The LCM of 30 and 24 will be the product of these numbers: LCM(30, 24) = 23 × 3 × 5 = 8 × 3 × 5 = 24 × 5 = 120. So, the least common multiple of 30 and 24 is 120.