If a number is divisible by both 8 and 12, which of the following must also be t

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Question: If a number is divisible by both 8 and 12, which of the following must also be true?

Options:

Correct Answer: It is divisible by 24.

Solution:

The least common multiple of 8 and 12 is 24, so any number divisible by both must also be divisible by 24.

If a number is divisible by both 8 and 12, which of the following must also be true?

If a number is divisible by both 8 and 12, which of the following must also be true?

Step 1: Understand what it means for a number to be divisible by another number. A number is divisible by another if you can divide them without leaving a remainder.
Step 2: Identify the numbers we are working with: 8 and 12.
Step 3: Find the least common multiple (LCM) of 8 and 12. The LCM is the smallest number that both 8 and 12 can divide into without a remainder.
Step 4: To find the LCM of 8 and 12, list the multiples of each number: Multiples of 8 are 8, 16, 24, 32, ... and multiples of 12 are 12, 24, 36, ...
Step 5: Look for the smallest number that appears in both lists of multiples. The smallest number is 24.
Step 6: Conclude that if a number is divisible by both 8 and 12, it must also be divisible by their LCM, which is 24.

Divisibility – Understanding the conditions under which a number can be divided by another without leaving a remainder.
Least Common Multiple (LCM) – The smallest multiple that is exactly divisible by two or more numbers.