Free LCM Calculator determines the least common multiple (LCM) between 40 and 52 the smallest integer that is 520 that is divisible by both numbers.

Least Common Multiple (LCM) of 40 and 52 is **520**.

LCM(40,52) = 520

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

- Least Common Multiple of 40 and 52 by Prime method
- Least Common Multiple of 40 and 52 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 40 and 52. First we will calculate the **prime factors of 40 and 52**.

**Prime Factorization of 40**

2 | 40 |

2 | 20 |

2 | 10 |

5 | 5 |

1 |

Prime factors of 40 are 2,5. Prime factorization of **40** in exponential form is:

40 = 2^{3}×5^{1}

**Prime Factorization of 52**

2 | 52 |

2 | 26 |

13 | 13 |

1 |

Prime factors of 52 are 2,13. Prime factorization of **52** in exponential form is:

52 = 2^{2}×13^{1}

Now multiplying the highest exponent prime factors to calculate the **LCM of 40 and 52**.

LCM(40,52) = 2^{3}×5^{1}×13^{1}

LCM(40,52) = 520

**Factors of 40**

List of positive integer factors of 40 that divides 40 without a remainder.

1, 2, 4, 5, 8, 10, 20, 40

**Factors of 52**

List of positive integer factors of 52 that divides 52 without a remainder.

1, 2, 4, 13, 26, 52

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

We need to calculate greatest common factor 40 and 52, than apply into the LCM equation.

GCF(40,52) = 4

LCM(40,52) = ( 40 × 52) / 4

LCM(40,52) = 2080 / 4

LCM(40,52) = 520

(i) The LCM of 52 and 40 is associative

LCM of 40 and 52 = LCM of 52 and 40

1. What is the LCM of 40 and 52?

Answer: LCM of 40 and 52 is 520.

2. What are the Factors of 40?

Answer: Factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40. There are 8 integers that are factors of 40. The greatest factor of 40 is 40.

3. What are the Factors of 52?

Answer: Factors of 52 are 1, 2, 4, 13, 26, 52. There are 6 integers that are factors of 52. The greatest factor of 52 is 52.

4. How to Find the LCM of 40 and 52?

Answer:

Least Common Multiple of 40 and 52 = 520

Step 1: Find the prime factorization of 40

40 = 2 x 2 x 2 x 5

Step 2: Find the prime factorization of 52

52 = 2 x 2 x 13

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

LCM = 520 = 2 x 2 x 2 x 5 x 13

Step 4: Therefore, the least common multiple of 40 and 52 is 520.