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What is LCM of 10, 15 | Prime factorisation, common factor

Q: What is the LCM of 10 and 15?

What is the LCM of 10 and 15? The answer is 30. LCM using prime factorisation, common factor, video tutorial & instructions for each step.

Prime Factorization Method

There are multiple ways to find the least common multiple of given integers. In this method, we find the prime factors of each number, and then take the highest power of each prime that appears in the factorization of either number for find LCM.

Find the prime factorization of each number:

10 = 2, 5

15 = 3, 5

Identify the highest powers of all prime numbers that appear in the factorization: $2^1 × 3^1 × 5^1$
To find LCM multiply these highest powers: LCM(10, 15) = $2^1 × 3^1 × 5^1$ = 30

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Listing All Common Factors Method

To find the Least Common Multiple (LCM) of 10 and 15 using the method of listing common multiples, follow these steps:

List some multiples of each number.
Identify the smallest multiple that is common to both lists.

Multiples of 10

10, 20, 30, 40, 50, 60, 70, 80, 90, 100,…

Multiples of 15

15, 30, 45, 60, 75, 90, 105, 120, 135, 150,…

Common multiples

Identify the common multiples from the lists above: 30, 60, 90,…

The smallest common multiple is 30.

The LCM of 10 and 15 using the common multiples method is 30.

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What is the LCM of 10 and 15?

Answer: The LCM of 10 and 15 is 30

Prime Factorization Method

Watch the Animated Step-by-Step Solution

Listing All Common Factors Method

Review Sub Calculations

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