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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.

Methods 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 at least 2 numbers are divisible.

  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.

Know how to find the lcm of 12 and 18 here.

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.

FAQs

1. What is the LCM of 10 and 15?

The Least Common Multiple (LCM) of 10 and 15 is 30. This is the smallest positive integer that is divisible by both 10 and 15 without leaving any remainder. 

2. How to Find the LCM of 10 and 15 Using Prime Factorization?

To find the LCM using prime factorization:

  • Prime factorization of 10: 2 × 5

  • Prime factorization of 15: 3 × 5​

The LCM is obtained by multiplying the highest powers of all prime factors present in either number:​ LCM = 2 × 3 × 5 = 30 

3. How to Find the LCM of 10 and 15 Using the Division Method?

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

  1. Divide both numbers by 2: 10 ÷ 2 = 5; 15 ÷ 2 = not divisible

  2. Divide the resulting numbers by 3: 5 ÷ 3 = not divisible; 15 ÷ 3 = 5

  3. Divide the resulting numbers by 5: 5 ÷ 5 = 1; 5 ÷ 5 = 1​

Multiply all the prime divisors used: 2 × 3 × 5 = 30

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