Free LCM Calculator determines the least common multiple (LCM) between 36 and 45 the smallest integer that is 180 that is divisible by both numbers.

Least Common Multiple (LCM) of 36 and 45 is **180**.

LCM(36,45) = 180

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

- Least Common Multiple of 36 and 45 by Prime method
- Least Common Multiple of 36 and 45 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 36 and 45. First we will calculate the **prime factors of 36 and 45**.

**Prime Factorization of 36**

2 | 36 |

2 | 18 |

3 | 9 |

3 | 3 |

1 |

Prime factors of 36 are 2,3. Prime factorization of **36** in exponential form is:

36 = 2^{2}×3^{2}

**Prime Factorization of 45**

3 | 45 |

3 | 15 |

5 | 5 |

1 |

Prime factors of 45 are 3,5. Prime factorization of **45** in exponential form is:

45 = 3^{2}×5^{1}

Now multiplying the highest exponent prime factors to calculate the **LCM of 36 and 45**.

LCM(36,45) = 2^{2}×3^{2}×5^{1}

LCM(36,45) = 180

**Factors of 36**

List of positive integer factors of 36 that divides 36 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36

**Factors of 45**

List of positive integer factors of 45 that divides 45 without a remainder.

1, 3, 5, 9, 15, 45

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

We need to calculate greatest common factor 36 and 45, than apply into the LCM equation.

GCF(36,45) = 9

LCM(36,45) = ( 36 × 45) / 9

LCM(36,45) = 1620 / 9

LCM(36,45) = 180

(i) The LCM of 45 and 36 is associative

LCM of 36 and 45 = LCM of 45 and 36

1. What is the LCM of 36 and 45?

Answer: LCM of 36 and 45 is 180.

2. What are the Factors of 36?

Answer: Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. There are 9 integers that are factors of 36. The greatest factor of 36 is 36.

3. What are the Factors of 45?

Answer: Factors of 45 are 1, 3, 5, 9, 15, 45. There are 6 integers that are factors of 45. The greatest factor of 45 is 45.

4. How to Find the LCM of 36 and 45?

Answer:

Least Common Multiple of 36 and 45 = 180

Step 1: Find the prime factorization of 36

36 = 2 x 2 x 3 x 3

Step 2: Find the prime factorization of 45

45 = 3 x 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 = 180 = 2 x 2 x 3 x 3 x 5

Step 4: Therefore, the least common multiple of 36 and 45 is 180.