What is the smallest number that is divisible by both 18 and 24?

What is the smallest number that is divisible by both 18 and 24?

Step 1: Identify the two numbers we want to find the smallest number for, which are 18 and 24.
Step 2: Find the prime factorization of each number.
Step 3: For 18, the prime factorization is 2 x 3 x 3 (or 2 x 3^2).
Step 4: For 24, the prime factorization is 2 x 2 x 2 x 3 (or 2^3 x 3).
Step 5: Identify the highest power of each prime number from both factorizations.
Step 6: The highest power of 2 is 2^3 (from 24) and the highest power of 3 is 3^2 (from 18).
Step 7: Multiply these highest powers together: 2^3 x 3^2.
Step 8: Calculate 2^3, which is 8, and 3^2, which is 9.
Step 9: Now multiply 8 and 9 together: 8 x 9 = 72.
Step 10: Therefore, the smallest number that is divisible by both 18 and 24 is 72.

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