What is the least common multiple (LCM) of 12 and 15?

What is the least common multiple (LCM) of 12 and 15?

• A. 40
• B. 60
• C. 75
• D. 90

Answer: (B)

To find the least common multiple (LCM) of 12 and 15, you can begin by determining the prime factorization of each number. The prime factorization of 12 is \(2^2 \times 3^1\), and the prime factorization of 15 is \(3^1 \times 5^1\). To find the LCM, you take the highest exponent of each prime number that appears in the factorizations. This means that you will use: - The highest power of 2, which is \(2^2\) from 12, - The highest power of 3, which is \(3^1\) from both numbers, - The highest power of 5, which is \(5^1\) from 15. Now, multiply these together to calculate the LCM: \[ LCM = 2^2 \times 3^1 \times 5^1 = 4 \times 3 \times 5. \] Calculating this step by step: 1. \(4 \times 3 = 12\), 2. Then \(12 \times 5 = 60\). Thus, the least common multiple of

To find the least common multiple (LCM) of 12 and 15, you can begin by determining the prime factorization of each number.

The prime factorization of 12 is (2^2 \times 3^1), and the prime factorization of 15 is (3^1 \times 5^1).

To find the LCM, you take the highest exponent of each prime number that appears in the factorizations. This means that you will use:

• The highest power of 2, which is (2^2) from 12,

• The highest power of 3, which is (3^1) from both numbers,

• The highest power of 5, which is (5^1) from 15.

Now, multiply these together to calculate the LCM:

[

LCM = 2^2 \times 3^1 \times 5^1 = 4 \times 3 \times 5.

]

Calculating this step by step:

1. (4 \times 3 = 12),

2. Then (12 \times 5 = 60).

Thus, the least common multiple of