Least Common Multiple of 400 and 408

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 408 the smallest integer that is 20400 that is divisible by both numbers.

Least Common Multiple (LCM) of 400 and 408 is 20400.

LCM(400,408) = 20400

LCM of 400 and 408

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

LCM of:
and

Least Common Multiple of 400 and 408

LCM of 400 and 408 is 20400

Least common multiple can be found by multiplying the highest exponent prime factors of 400 and 408. First we will calculate the prime factors of 400 and 408.

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 408


2 408
2 204
2 102
3 51
17 17
1

Prime factors of 408 are 2, 3,17. Prime factorization of 408 in exponential form is:

408 = 23×31×171

Now multiplying the highest exponent prime factors to calculate the LCM of 400 and 408.

LCM(400,408) = 24×31×52×171
LCM(400,408) = 20400

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 408

List of positive integer factors of 408 that divides 408 without a remainder.

1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408

Least Common Multiple of 400 and 408 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 408, than apply into the LCM equation.

GCF(400,408) = 8
LCM(400,408) = ( 400 × 408) / 8
LCM(400,408) = 163200 / 8
LCM(400,408) = 20400

Properties of LCM 400 and 408

(i) The LCM of 408 and 400 is associative

LCM of 400 and 408 = LCM of 408 and 400

Related Least Common Multiples of 400

Related Least Common Multiples of 408

Frequently Asked Questions on LCM of 400 and 408

1. What is the LCM of 400 and 408?

Answer: LCM of 400 and 408 is 20400.

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 408?

Answer: Factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408. There are 16 integers that are factors of 408. The greatest factor of 408 is 408.

4. How to Find the LCM of 400 and 408?

Answer:

Least Common Multiple of 400 and 408 = 20400

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 408

408 = 2 x 2 x 2 x 3 x 17

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

LCM = 20400 = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 17

Step 4: Therefore, the least common multiple of 400 and 408 is 20400.