lcm of 3 and 20

Steps to Solve

1. Find the prime factorization of each number

First, we need to find the prime factorization of both numbers:

• For the number 3, the prime factorization is (3^1).
• For the number 20, we can factor it: (20 = 2 \times 10 = 2 \times 2 \times 5 = 2^2 \times 5^1).

2. Identify the highest powers of all prime factors

Next, we take all the prime factors that appear in the factorizations and choose the highest power of each:

• The prime factors we have are 2, 3, and 5.
• The highest power of 2 is (2^2).
• The highest power of 3 is (3^1).
• The highest power of 5 is (5^1).

3. Multiply the highest powers together

Now we multiply the highest powers of these prime factors to find the LCM:

$$ \text{LCM} = 2^2 \times 3^1 \times 5^1 $$

Calculating this gives:

$$ \text{LCM} = 4 \times 3 \times 5 $$

4. Perform the multiplication step-by-step

First, multiply (4) and (3):

$$ 4 \times 3 = 12 $$

Then multiply the result by (5):

$$ 12 \times 5 = 60 $$

5. Conclusion

The least common multiple of 3 and 20 is (60).