Orchids Logo
Admissions 2025-26
9-999-431-999info@orchids.edu.inWhatsapp
Login
Doubt Connect
Orchids Logo

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.

Methods 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 at least 2 numbers are divisible.

  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.

Know how to find the lcm of 24 and 36 here.

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.

FAQs

1. What is the LCM of 15 and 20?

The LCM of 15 and 20 is 60. This is the smallest positive integer that is divisible by both 15 and 20 without leaving any remainder.

2. How to Find the LCM of 15 and 20 Using Prime Factorization?

To find the LCM using prime factorization:

  • Prime factorization of 15: 3 × 5

  • Prime factorization of 20: 2 × 2 × 5​

The LCM is obtained by multiplying the highest powers of all prime factors present in either number:​

LCM = 2² × 3 × 5 = 60 ​

3. How to Find the LCM of 15 and 20 Using the Division Method?

The division method involves dividing the numbers by their common prime factors:

  1. Divide both numbers by 2 (if possible).

  2. Divide the resulting numbers by 3 (if possible).

  3. Continue dividing by prime numbers until all resulting numbers are 1.​

The LCM is the product of all the prime numbers used in the division. For 15 and 20, this results in:​ LCM = 2 × 2 × 3 × 5 = 60

Share