If a number is divisible by both 4 and 6, which of the following must also be tr

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Question: If a number is divisible by both 4 and 6, which of the following must also be true? (2023)

Options:

Correct Answer: It is divisible by 12.

Exam Year: 2023

Solution:

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

If a number is divisible by both 4 and 6, which of the following must also be true? (2023)

If a number is divisible by both 4 and 6, which of the following must also be true? (2023)

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: 4 and 6.
Step 3: Find the least common multiple (LCM) of 4 and 6. The LCM is the smallest number that both 4 and 6 can divide into evenly.
Step 4: List the multiples of 4: 4, 8, 12, 16, 20, ...
Step 5: List the multiples of 6: 6, 12, 18, 24, ...
Step 6: Find the smallest number that appears in both lists. The smallest number is 12.
Step 7: Conclude that if a number is divisible by both 4 and 6, it must also be divisible by their LCM, which is 12.

Divisibility – Understanding the rules of divisibility for numbers, particularly 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.