Free LCM Calculator determines the least common multiple (LCM) between 10 and 15 the smallest integer that is 30 that is divisible by both numbers.

Least Common Multiple (LCM) of 10 and 15 is **30**.

LCM(10,15) = 30

*Least common multiple* or lowest common denominator (LCD) can be calculated in three ways;

- Least Common Multiple of 10 and 15 by Prime method
- Least Common Multiple of 10 and 15 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 10 and 15. First we will calculate the **prime factors of 10 and 15**.

**Prime Factorization of 10**

2 | 10 |

5 | 5 |

1 |

Prime factors of 10 are 2,5. Prime factorization of **10** in exponential form is:

10 = 2^{1}×5^{1}

**Prime Factorization of 15**

3 | 15 |

5 | 5 |

1 |

Prime factors of 15 are 3,5. Prime factorization of **15** in exponential form is:

15 = 3^{1}×5^{1}

Now multiplying the highest exponent prime factors to calculate the **LCM of 10 and 15**.

LCM(10,15) = 2^{1}×3^{1}×5^{1}

LCM(10,15) = 30

**Factors of 10**

List of positive integer factors of 10 that divides 10 without a remainder.

1, 2, 5, 10

**Factors of 15**

List of positive integer factors of 15 that divides 15 without a remainder.

1, 3, 5, 15

The formula of **LCM** is LCM(a,b) = ( a × b) / GCF(a,b).

We need to calculate greatest common factor 10 and 15, than apply into the LCM equation.

GCF(10,15) = 5

LCM(10,15) = ( 10 × 15) / 5

LCM(10,15) = 150 / 5

LCM(10,15) = 30

(i) The LCM of 15 and 10 is associative

LCM of 10 and 15 = LCM of 15 and 10

1. What is the LCM of 10 and 15?

Answer: LCM of 10 and 15 is 30.

2. What are the Factors of 10?

Answer: Factors of 10 are 1, 2, 5, 10. There are 4 integers that are factors of 10. The greatest factor of 10 is 10.

3. What are the Factors of 15?

Answer: Factors of 15 are 1, 3, 5, 15. There are 4 integers that are factors of 15. The greatest factor of 15 is 15.

4. How to Find the LCM of 10 and 15?

Answer:

Least Common Multiple of 10 and 15 = 30

Step 1: Find the prime factorization of 10

10 = 2 x 5

Step 2: Find the prime factorization of 15

15 = 3 x 5

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 30 = 2 x 3 x 5

Step 4: Therefore, the least common multiple of 10 and 15 is 30.