Least Common Multiple of 400 and 402

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 400 and 402 the smallest integer that is 80400 that is divisible by both numbers.

Least Common Multiple (LCM) of 400 and 402 is 80400.

LCM(400,402) = 80400

LCM of 400 and 402

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

LCM of:
and

Least Common Multiple of 400 and 402

LCM of 400 and 402 is 80400

Least common multiple can be found by multiplying the highest exponent prime factors of 400 and 402. First we will calculate the prime factors of 400 and 402.

Prime Factorization of 400


2 400
2 200
2 100
2 50
5 25
5 5
1

Prime factors of 400 are 2,5. Prime factorization of 400 in exponential form is:

400 = 24×52

Prime Factorization of 402


2 402
3 201
67 67
1

Prime factors of 402 are 2, 3,67. Prime factorization of 402 in exponential form is:

402 = 21×31×671

Now multiplying the highest exponent prime factors to calculate the LCM of 400 and 402.

LCM(400,402) = 24×31×52×671
LCM(400,402) = 80400

Factors of 400

List of positive integer factors of 400 that divides 400 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400

Factors of 402

List of positive integer factors of 402 that divides 402 without a remainder.

1, 2, 3, 6, 67, 134, 201, 402

Least Common Multiple of 400 and 402 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 400 and 402, than apply into the LCM equation.

GCF(400,402) = 2
LCM(400,402) = ( 400 × 402) / 2
LCM(400,402) = 160800 / 2
LCM(400,402) = 80400

Properties of LCM 400 and 402

(i) The LCM of 402 and 400 is associative

LCM of 400 and 402 = LCM of 402 and 400

Related Least Common Multiples of 400

Related Least Common Multiples of 402

Frequently Asked Questions on LCM of 400 and 402

1. What is the LCM of 400 and 402?

Answer: LCM of 400 and 402 is 80400.

2. What are the Factors of 400?

Answer: Factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400. There are 15 integers that are factors of 400. The greatest factor of 400 is 400.

3. What are the Factors of 402?

Answer: Factors of 402 are 1, 2, 3, 6, 67, 134, 201, 402. There are 8 integers that are factors of 402. The greatest factor of 402 is 402.

4. How to Find the LCM of 400 and 402?

Answer:

Least Common Multiple of 400 and 402 = 80400

Step 1: Find the prime factorization of 400

400 = 2 x 2 x 2 x 2 x 5 x 5

Step 2: Find the prime factorization of 402

402 = 2 x 3 x 67

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

LCM = 80400 = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 67

Step 4: Therefore, the least common multiple of 400 and 402 is 80400.