If a number is divisible by both 3 and 4, which of the following must also be tr

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Question: If a number is divisible by both 3 and 4, which of the following must also be true?

Options:

Correct Answer: It is divisible by 12.

Solution:

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

If a number is divisible by both 3 and 4, which of the following must also be true?

If a number is divisible by both 3 and 4, 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 it by that number without leaving a remainder.
Step 2: Identify the numbers we are working with, which are 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 evenly.
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 divisible by both 3 and 4, it must also be divisible by their LCM, which is 12.

Divisibility – Understanding the rules of divisibility for numbers, specifically how to determine if a number is divisible by multiple integers.
Least Common Multiple (LCM) – The concept of finding the least common multiple of two or more numbers, which is the smallest number that is a multiple of each of the numbers.