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

₹0.0

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

Options:

Correct Answer: 60

Exam Year: 2023

Solution:

The LCM of 12 and 15 is 60, which is the smallest number divisible by both.

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

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

Step 1: Understand that we need to find a number that can be divided evenly by both 12 and 15.
Step 2: Find the prime factorization of 12. It is 2 x 2 x 3 (or 2^2 x 3).
Step 3: Find the prime factorization of 15. It is 3 x 5.
Step 4: To find the LCM (Least Common Multiple), take the highest power of each prime number from both factorizations.
Step 5: From 12, we have 2^2 and 3. From 15, we have 3 and 5.
Step 6: The highest power of 2 is 2^2, the highest power of 3 is 3, and the highest power of 5 is 5.
Step 7: Multiply these together: 2^2 (which is 4) x 3 x 5.
Step 8: Calculate 4 x 3 = 12.
Step 9: Now calculate 12 x 5 = 60.
Step 10: Therefore, the smallest number that is divisible by both 12 and 15 is 60.

Least Common Multiple (LCM) – The smallest positive integer that is divisible by two or more numbers.
Divisibility Rules – Understanding how to determine if a number is divisible by another number.