Least Common Multiple of 400 and 404

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 404 the smallest integer that is 40400 that is divisible by both numbers.

Least Common Multiple (LCM) of 400 and 404 is 40400.

LCM(400,404) = 40400

LCM of 400 and 404

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

LCM of:
and

Least Common Multiple of 400 and 404

LCM of 400 and 404 is 40400

Least common multiple can be found by multiplying the highest exponent prime factors of 400 and 404. First we will calculate the prime factors of 400 and 404.

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 404


2 404
2 202
101 101
1

Prime factors of 404 are 2,101. Prime factorization of 404 in exponential form is:

404 = 22×1011

Now multiplying the highest exponent prime factors to calculate the LCM of 400 and 404.

LCM(400,404) = 24×52×1011
LCM(400,404) = 40400

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 404

List of positive integer factors of 404 that divides 404 without a remainder.

1, 2, 4, 101, 202, 404

Least Common Multiple of 400 and 404 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 404, than apply into the LCM equation.

GCF(400,404) = 4
LCM(400,404) = ( 400 × 404) / 4
LCM(400,404) = 161600 / 4
LCM(400,404) = 40400

Properties of LCM 400 and 404

(i) The LCM of 404 and 400 is associative

LCM of 400 and 404 = LCM of 404 and 400

Related Least Common Multiples of 400

Related Least Common Multiples of 404

Frequently Asked Questions on LCM of 400 and 404

1. What is the LCM of 400 and 404?

Answer: LCM of 400 and 404 is 40400.

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 404?

Answer: Factors of 404 are 1, 2, 4, 101, 202, 404. There are 6 integers that are factors of 404. The greatest factor of 404 is 404.

4. How to Find the LCM of 400 and 404?

Answer:

Least Common Multiple of 400 and 404 = 40400

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 404

404 = 2 x 2 x 101

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

LCM = 40400 = 2 x 2 x 2 x 2 x 5 x 5 x 101

Step 4: Therefore, the least common multiple of 400 and 404 is 40400.