A number is divisible by both 6 and 8. What is the smallest number that is also

₹0.0

Question: A number is divisible by both 6 and 8. What is the smallest number that is also divisible by 12? (2023)

Options:

Correct Answer: 24

Exam Year: 2023

Solution:

The LCM of 6 and 8 is 24, which is also divisible by 12. Hence, the smallest number is 24.

A number is divisible by both 6 and 8. What is the smallest number that is also divisible by 12? (2023)

A number is divisible by both 6 and 8. What is the smallest number that is also divisible by 12? (2023)

Step 1: Understand that a number is divisible by another number if it can be divided by that number without leaving a remainder.
Step 2: Identify the numbers we are working with: 6 and 8.
Step 3: Find the Least Common Multiple (LCM) of 6 and 8. The LCM is the smallest number that both 6 and 8 can divide into evenly.
Step 4: List the multiples of 6: 6, 12, 18, 24, 30, ...
Step 5: List the multiples of 8: 8, 16, 24, 32, ...
Step 6: Find the smallest number that appears in both lists. The smallest common multiple is 24.
Step 7: Check if 24 is also divisible by 12. Since 24 divided by 12 equals 2 with no remainder, it is divisible.
Step 8: Conclude that the smallest number that is divisible by both 6 and 8, and also by 12, is 24.

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