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

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

Options:

Correct Answer: 72

Solution:

The LCM of 18 and 24 is 72, which is the smallest number divisible by both.

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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