If a number is a multiple of both 3 and 4, which of the following is guaranteed

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Question: If a number is a multiple of both 3 and 4, which of the following is guaranteed to be true?

Options:

Correct Answer: It is a multiple of 12.

Solution:

The least common multiple of 3 and 4 is 12, so any multiple of both must also be a multiple of 12.

If a number is a multiple of both 3 and 4, which of the following is guaranteed to be true?

If a number is a multiple of both 3 and 4, which of the following is guaranteed to 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 in the question. We are looking at the numbers 3 and 4.
Step 3: Find the least common multiple (LCM) of 3 and 4. The LCM is the smallest number that both 3 and 4 can divide into without leaving a remainder.
Step 4: Calculate the LCM of 3 and 4. The multiples of 3 are 3, 6, 9, 12, 15, ... and the multiples of 4 are 4, 8, 12, 16, ... The smallest number that appears in both lists is 12.
Step 5: Conclude that if a number is a multiple of both 3 and 4, it must also be a multiple of their LCM, which is 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.