If a number is divisible by both 3 and 5, which of the following is guaranteed t

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Question: If a number is divisible by both 3 and 5, which of the following is guaranteed to be true?

Options:

Correct Answer: It is divisible by 15

Solution:

A number divisible by both 3 and 5 is also divisible by their least common multiple, which is 15.

If a number is divisible by both 3 and 5, which of the following is guaranteed to be true?

If a number is divisible by both 3 and 5, which of the following is guaranteed to 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 two numbers in the question: 3 and 5.
Step 3: Find the least common multiple (LCM) of 3 and 5. The LCM is the smallest number that both 3 and 5 can divide into without a remainder.
Step 4: Calculate the LCM of 3 and 5. The multiples of 3 are 3, 6, 9, 12, 15, ... and the multiples of 5 are 5, 10, 15, ... The smallest number that appears in both lists is 15.
Step 5: Conclude that if a number is divisible by both 3 and 5, it must also be divisible by 15, since 15 is the LCM of 3 and 5.

Divisibility – Understanding the rules of divisibility, particularly how to determine if a number is divisible by multiple integers.
Least Common Multiple (LCM) – The concept that if a number is divisible by two integers, it is also divisible by their least common multiple.