**Created By :**
Jatin Gogia

**Reviewed By :**
Rajasekhar Valipishetty

**Last Updated :**
Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 2400 and 2402 the smallest integer that is 2882400 that is divisible by both numbers.

Least Common Multiple (LCM) of 2400 and 2402 is **2882400**.

LCM(2400,2402) = 2882400

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

Least common multiple can be found by multiplying the highest exponent prime factors of 2400 and 2402. First we will calculate the **prime factors of 2400 and 2402**.

**Prime Factorization of 2400**

2 | 2400 |

2 | 1200 |

2 | 600 |

2 | 300 |

2 | 150 |

3 | 75 |

5 | 25 |

5 | 5 |

1 |

Prime factors of 2400 are 2, 3,5. Prime factorization of **2400** in exponential form is:

2400 = 2^{5}×3^{1}×5^{2}

**Prime Factorization of 2402**

2 | 2402 |

1201 | 1201 |

1 |

Prime factors of 2402 are 2,1201. Prime factorization of **2402** in exponential form is:

2402 = 2^{1}×1201^{1}

Now multiplying the highest exponent prime factors to calculate the **LCM of 2400 and 2402**.

LCM(2400,2402) = 2^{5}×3^{1}×5^{2}×1201^{1}

LCM(2400,2402) = 2882400

**Factors of 2400**

List of positive integer factors of 2400 that divides 2400 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 75, 80, 96, 100, 120, 150, 160, 200, 240, 300, 400, 480, 600, 800, 1200, 2400

**Factors of 2402**

List of positive integer factors of 2402 that divides 2402 without a remainder.

1, 2, 1201, 2402

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

We need to calculate greatest common factor 2400 and 2402, than apply into the LCM equation.

GCF(2400,2402) = 2

LCM(2400,2402) = ( 2400 × 2402) / 2

LCM(2400,2402) = 5764800 / 2

LCM(2400,2402) = 2882400

(i) The LCM of 2402 and 2400 is associative

LCM of 2400 and 2402 = LCM of 2402 and 2400

1. What is the LCM of 2400 and 2402?

Answer: LCM of 2400 and 2402 is 2882400.

2. What are the Factors of 2400?

Answer: Factors of 2400 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 75, 80, 96, 100, 120, 150, 160, 200, 240, 300, 400, 480, 600, 800, 1200, 2400. There are 36 integers that are factors of 2400. The greatest factor of 2400 is 2400.

3. What are the Factors of 2402?

Answer: Factors of 2402 are 1, 2, 1201, 2402. There are 4 integers that are factors of 2402. The greatest factor of 2402 is 2402.

4. How to Find the LCM of 2400 and 2402?

Answer:

Least Common Multiple of 2400 and 2402 = 2882400

Step 1: Find the prime factorization of 2400

2400 = 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5

Step 2: Find the prime factorization of 2402

2402 = 2 x 1201

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

LCM = 2882400 = 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5 x 1201

Step 4: Therefore, the least common multiple of 2400 and 2402 is 2882400.