If a number is divisible by both 9 and 12, which of the following is guaranteed

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Question: If a number is divisible by both 9 and 12, which of the following is guaranteed to be true?

Options:

Correct Answer: It is divisible by 18.

Solution:

The least common multiple of 9 and 12 is 36, and since 36 is divisible by 18, the number must also be divisible by 18.

If a number is divisible by both 9 and 12, which of the following is guaranteed to be true?

If a number is divisible by both 9 and 12, 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 them without leaving a remainder.
Step 2: Identify the numbers we are working with: 9 and 12.
Step 3: Find the least common multiple (LCM) of 9 and 12. The LCM is the smallest number that both 9 and 12 can divide into without a remainder.
Step 4: Calculate the LCM of 9 and 12. The multiples of 9 are 9, 18, 27, 36, ... and the multiples of 12 are 12, 24, 36, ... The smallest common multiple is 36.
Step 5: Now that we know the LCM is 36, we check if 36 is divisible by 18. Since 36 divided by 18 equals 2 with no remainder, 36 is divisible by 18.
Step 6: Since the number we are considering is divisible by both 9 and 12, it must also be divisible by their LCM, which is 36. Therefore, it is also divisible by 18.

Divisibility Rules – Understanding the conditions under which numbers are divisible by other numbers.
Least Common Multiple (LCM) – Finding the smallest number that is a multiple of two or more numbers.
Prime Factorization – Breaking down numbers into their prime factors to analyze divisibility.