A number is divisible by both 12 and 15. What is the smallest number that is als

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Question: A number is divisible by both 12 and 15. What is the smallest number that is also divisible by 36? (2023)

Options:

Correct Answer: 180

Exam Year: 2023

Solution:

The LCM of 12 and 15 is 60. The smallest number divisible by 60 and 36 is 180.

A number is divisible by both 12 and 15. What is the smallest number that is also divisible by 36? (2023)

A number is divisible by both 12 and 15. What is the smallest number that is also divisible by 36? (2023)

Step 1: Find the Least Common Multiple (LCM) of 12 and 15.
Step 2: To find the LCM, list the multiples of 12: 12, 24, 36, 48, 60, ...
Step 3: List the multiples of 15: 15, 30, 45, 60, 75, ...
Step 4: Identify the smallest common multiple from both lists. The smallest common multiple is 60.
Step 5: Now, we need to find the smallest number that is divisible by both 60 and 36.
Step 6: List the multiples of 60: 60, 120, 180, ...
Step 7: List the multiples of 36: 36, 72, 108, 144, 180, ...
Step 8: Identify the smallest common multiple from both lists. The smallest common multiple is 180.

Least Common Multiple (LCM) – The LCM of two or more numbers is the smallest number that is a multiple of each of the numbers.
Divisibility Rules – Understanding the conditions under which a number is divisible by another number.