LCM of 15 and 20: How to find LCM of 15 and 20?

The LCM of 15 and 20 is 60. Least Common Multiple (LCM) of two numbers is the smallest number that both can multiply into. The LCM of 15 and 20 is the smallest number that both 15 and 20 fit into. In this blog, we’ll explain easy ways to find the LCM of 15 and 20.

How to Find the LCM of 15 and 20

Here are three simple methods to find the LCM of 15 and 20:

1. Prime Factorization Method

We break each number into its prime factors and take the highest power of each factor.

• 15 = 3 × 5
• 20 = 2 × 2 × 5
• Using the highest powers: 2² × 3 × 5 = 60

Thus, LCM(15,20) = 60.

2. Listing Multiples Method

We list the multiples of both numbers and find the smallest one they share.

• Multiples of 15: 15, 30, 45, 60, 75, ...
• Multiples of 20: 20, 40, 60, 80, 100, ...
• The smallest common multiple is 60.

Thus, LCM(15,20) = 60.

3. Division Method

We divide both numbers by their common factors until we get 1.

1. Divide 15 and 20 by 2 → (15, 10)
2. Divide 15 and 10 by 2 → (15, 5)
3. Divide 15 and 5 by 5 → (3, 1)
4. Both 3 and 1 are only divisible by 1
5. Multiply the divisors: 2 × 2 × 3 × 5 = 60

Thus, LCM(15,20) = 60.

Conclusion

The LCM of 15 and 20 is 60, and you can find it using prime factorization, listing multiples, or division. These methods make LCM calculations easy and useful.