Question

LCM of the numbers 12 and 20 will be :

• A. 30
• B. 60
• C. 120
• D. 140

Hint:

For small numbers, you can just list multiples: 12, 24, 36, 48, {60}... and 20, 40, {60}. The first match is the LCM.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The Least Common Multiple (LCM) is the smallest positive integer that is divisible by both numbers. We can find this by identifying the prime factors and taking the highest power of each.
Step 2: Prime Factorization:

$12 = 2 \times 2 \times 3 = 2^2 \times 3$
$20 = 2 \times 2 \times 5 = 2^2 \times 5$
Step 3: Calculating the LCM:
To find the LCM, we take the product of the highest powers of all prime factors present: \[ \text{LCM} = 2^2 \times 3 \times 5 = 4 \times 3 \times 5 = 60 \]
Step 4: Final Answer:
The LCM of 12 and 20 is 60.