Question

Using prime factorisation method find the LCM of 12 and 20

Answer 1

To find the Least Common Multiple (LCM) of 12 and 20 using the prime factorization method, we first need to find the prime factorization of each number.

**Step 1: Prime Factorization**

1. **Prime factorization of 12:**
- 12 can be divided by 2: \( 12 ÷ 2 = 6 \)
- 6 can be divided by 2: \( 6 ÷ 2 = 3 \)
- 3 is a prime number.
- Therefore, the prime factorization of 12 is:
\[
12 = 2^2 × 3^1
\]

2. **Prime factorization of 20:**
- 20 can be divided by 2: \( 20 ÷ 2 = 10 \)
- 10 can be divided by 2: \( 10 ÷ 2 = 5 \)
- 5 is a prime number.
- Therefore, the prime factorization of 20 is:
\[
20 = 2^2 × 5^1
\]

**Step 2: LCM Calculation**

To find the LCM, we take the highest power of each prime factor that appears in the factorizations.

- For the prime number **2**: The highest power is \( 2^2 \).
- For the prime number **3**: The highest power is \( 3^1 \).
- For the prime number **5**: The highest power is \( 5^1 \).

Now, we multiply these together:
\[
\text{LCM} = 2^2 × 3^1 × 5^1
\]

Calculating this:
\[
= 4 × 3 × 5
\]
\[
= 12 × 5
\]
\[
= 60
\]

Therefore, the LCM of 12 and 20 is **60**.