LCM of 10 and 15: How to find LCM of 10 and 15?

The LCM of 10 and 15 is 30. Least Common Multiple (LCM) of two numbers is the smallest number that is a multiple of both. The LCM of 10 and 15 is the smallest number that both 10 and 15 fit into. In this blog, we’ll explain easy ways to find the LCM of 10 and 15.

How to Find the LCM of 10 and 15

Here are three simple methods to find the LCM of 10 and 15:

1. Prime Factorization Method

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

• 10 = 2 × 5
• 15 = 3 × 5
• Taking the highest powers: 2 × 3 × 5 = 30

Thus, LCM(10,15) = 30.

2. Listing Multiples Method

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

• Multiples of 10: 10, 20, 30, 40, 50, ...
• Multiples of 15: 15, 30, 45, 60, ...
• The smallest common multiple is 30.

Thus, LCM(10,15) = 30.

3. Division Method

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

1. Divide 10 and 15 by 5 → (2, 3)
2. Both 2 and 3 are only divisible by 1
3. Multiply the divisors: 2 × 3 × 5 = 30

Thus, LCM(10,15) = 30.

Conclusion

The LCM of 10 and 15 is 30, and you can find it using prime factorization, listing multiples, or division. These methods make LCM calculations simple and useful.