If a number is divisible by both 2 and 5, which of the following must be true?

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Question: If a number is divisible by both 2 and 5, which of the following must be true?

Options:

Correct Answer: It is divisible by 10

Solution:

A number divisible by both 2 and 5 is also divisible by 10, as 10 is the least common multiple of 2 and 5.

If a number is divisible by both 2 and 5, which of the following must be true?

If a number is divisible by both 2 and 5, which of the following must be true?

Step 1: Understand what it means for a number to be divisible by 2. A number is divisible by 2 if it is even, meaning it ends in 0, 2, 4, 6, or 8.
Step 2: Understand what it means for a number to be divisible by 5. A number is divisible by 5 if it ends in 0 or 5.
Step 3: If a number is divisible by both 2 and 5, it must end in 0 because 0 is the only digit that satisfies both conditions (even and ends in 5).
Step 4: Recognize that any number that ends in 0 is also divisible by 10, since 10 is the smallest number that can be formed by multiplying 2 and 5 together.
Step 5: Conclude that if a number is divisible by both 2 and 5, it must also be divisible by 10.

Divisibility Rules – Understanding the rules of divisibility, particularly how numbers divisible by 2 and 5 are also divisible by their least common multiple, which is 10.
Least Common Multiple (LCM) – The concept of LCM and how it applies to determining divisibility by multiple numbers.