If a number is a multiple of both 4 and 6, which of the following must also be t

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Question: If a number is a multiple of both 4 and 6, which of the following must also be true?

Options:

Correct Answer: It is a multiple of 12.

Solution:

The least common multiple of 4 and 6 is 12, so any number that is a multiple of both must also be a multiple of 12.

If a number is a multiple of both 4 and 6, which of the following must also be true?

If a number is a multiple of both 4 and 6, which of the following must also be true?

Step 1: Understand what a multiple is. A multiple of a number is the result of multiplying that number by an integer (like 1, 2, 3, etc.).
Step 2: Identify the numbers we are working with: 4 and 6.
Step 3: Find the multiples of 4: 4, 8, 12, 16, 20, ...
Step 4: Find the multiples of 6: 6, 12, 18, 24, ...
Step 5: Look for the smallest number that appears in both lists of multiples. This is called the least common multiple (LCM).
Step 6: The smallest number that is a multiple of both 4 and 6 is 12.
Step 7: Conclude that if a number is a multiple of both 4 and 6, it must also be a multiple of 12.

Multiples and Least Common Multiple (LCM) – Understanding that a number that is a multiple of two numbers must also be a multiple of their least common multiple.