Least Common Multiple of 400 and 420

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 420 the smallest integer that is 8400 that is divisible by both numbers.

Least Common Multiple (LCM) of 400 and 420 is 8400.

LCM(400,420) = 8400

LCM of 400 and 420

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

LCM of:
and

Least Common Multiple of 400 and 420

LCM of 400 and 420 is 8400

Least common multiple can be found by multiplying the highest exponent prime factors of 400 and 420. First we will calculate the prime factors of 400 and 420.

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 420


2 420
2 210
3 105
5 35
7 7
1

Prime factors of 420 are 2, 3, 5,7. Prime factorization of 420 in exponential form is:

420 = 22×31×51×71

Now multiplying the highest exponent prime factors to calculate the LCM of 400 and 420.

LCM(400,420) = 24×31×52×71
LCM(400,420) = 8400

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 420

List of positive integer factors of 420 that divides 420 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420

Least Common Multiple of 400 and 420 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 420, than apply into the LCM equation.

GCF(400,420) = 20
LCM(400,420) = ( 400 × 420) / 20
LCM(400,420) = 168000 / 20
LCM(400,420) = 8400

Properties of LCM 400 and 420

(i) The LCM of 420 and 400 is associative

LCM of 400 and 420 = LCM of 420 and 400

Related Least Common Multiples of 400

Related Least Common Multiples of 420

Frequently Asked Questions on LCM of 400 and 420

1. What is the LCM of 400 and 420?

Answer: LCM of 400 and 420 is 8400.

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 420?

Answer: Factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420. There are 24 integers that are factors of 420. The greatest factor of 420 is 420.

4. How to Find the LCM of 400 and 420?

Answer:

Least Common Multiple of 400 and 420 = 8400

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 420

420 = 2 x 2 x 3 x 5 x 7

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

LCM = 8400 = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 7

Step 4: Therefore, the least common multiple of 400 and 420 is 8400.