If a number is divisible by both 4 and 6, what is the smallest positive integer

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Question: If a number is divisible by both 4 and 6, what is the smallest positive integer that is also divisible by 12?

Options:

Correct Answer: 12

Solution:

The least common multiple of 4 and 6 is 12.

If a number is divisible by both 4 and 6, what is the smallest positive integer that is also divisible by 12?

If a number is divisible by both 4 and 6, what is the smallest positive integer that is also divisible by 12?

Correct Answer: 12

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: Calculate the LCM of 4 and 6. The multiples of 4 are 4, 8, 12, 16, ... and the multiples of 6 are 6, 12, 18, ... The smallest number that appears in both lists is 12.
Step 5: Since 12 is the LCM of 4 and 6, it is also divisible by both 4 and 6.
Step 6: Finally, since we are looking for the smallest positive integer that is divisible by 12, the answer is 12 itself.

Divisibility and Least Common Multiple (LCM) – Understanding how to find the least common multiple of numbers and the relationship between divisibility.