Question

What is the least common multiple (LCM) of 10 and 12?
A.
40
B.
60
C.
2
D.
120

Answer 1

To find the least common multiple (LCM) of 10 and 12, we can use the prime factorization method.

1. **Prime factorization**:
- The prime factorization of 10 is \(2^1 \times 5^1\).
- The prime factorization of 12 is \(2^2 \times 3^1\).

2. **Take the highest power of each prime number**:
- For the prime number 2: the highest power is \(2^2\) (from 12).
- For the prime number 3: the highest power is \(3^1\) (from 12).
- For the prime number 5: the highest power is \(5^1\) (from 10).

3. **Multiply these together**:
\[
LCM = 2^2 \times 3^1 \times 5^1 = 4 \times 3 \times 5
\]
Now, calculate the product step by step:
- First, \(4 \times 3 = 12\).
- Then, \(12 \times 5 = 60\).

Therefore, the least common multiple (LCM) of 10 and 12 is \(60\).

The answer is **B. 60**.