Question

L.C.M. of 15, 18 and 24 is

• A. 90
• B. 120
• C. 240
• D. 360

Hint:

To quickly check your answer in a multiple-choice setting, verify if the correct option is divisible by all the given numbers (15, 18, and 24). For instance, 360/15 = 24, 360/18 = 20, and 360/24 = 15. This confirms it's a common multiple. To ensure it's the *least* common multiple, check if smaller options work (they don't).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The question asks for the Least Common Multiple (L.C.M.) of the numbers 15, 18, and 24. The L.C.M. is the smallest positive integer that is a multiple of all the given numbers.
Step 2: Key Formula or Approach:
We will use the prime factorization method to find the L.C.M. The L.C.M. is the product of the highest powers of all prime factors that appear in any of the numbers.
Step 3: Detailed Explanation:
First, find the prime factorization of each number.
\[ 15 = 3 \times 5 = 3^1 \times 5^1 \] \[ 18 = 2 \times 9 = 2^1 \times 3^2 \] \[ 24 = 2 \times 12 = 2 \times 2 \times 6 = 2 \times 2 \times 2 \times 3 = 2^3 \times 3^1 \] Now, identify the highest power of each prime factor present in the factorizations.
The prime factors are 2, 3, and 5.
Highest power of 2 is \( 2^3 \).
Highest power of 3 is \( 3^2 \).
Highest power of 5 is \( 5^1 \).
To find the L.C.M., multiply these highest powers together.
\[ \text{L.C.M.} = 2^3 \times 3^2 \times 5^1 \] \[ \text{L.C.M.} = 8 \times 9 \times 5 \] \[ \text{L.C.M.} = 72 \times 5 \] \[ \text{L.C.M.} = 360 \] Step 4: Final Answer:
The L.C.M. of 15, 18, and 24 is 360.