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

To find the Least Common Multiple (LCM) of the numbers 12 and 20, we can follow these steps:

First, we find the prime factorization of each number:

• The prime factors of 12 are: \(12 = 2^2 \times 3\)
• The prime factors of 20 are: \(20 = 2^2 \times 5\)

Next, identify the highest power of each prime number present in the factorizations:

• The highest power of 2 in both factorizations is \(2^2\).
• The highest power of 3 is \(3^1\).
• The highest power of 5 is \(5^1\).

Multiply these together to find the LCM:

The LCM is: \(2^2 \times 3^1 \times 5^1 = 4 \times 3 \times 5 = 60\)

Thus, the LCM of 12 and 20 is 60, which matches the correct answer provided: 60.

To verify, check the multiples:

• Multiples of 12: 12, 24, 36, 48, 60, 72, ...
• Multiples of 20: 20, 40, 60, 80, ...

The first common multiple is 60.

Therefore, the LCM of 12 and 20 is 60, confirming the given correct answer is accurate.