Least Common Multiple of 400 and 405

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 405 the smallest integer that is 32400 that is divisible by both numbers.

Least Common Multiple (LCM) of 400 and 405 is 32400.

LCM(400,405) = 32400

LCM of 400 and 405

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

LCM of:
and

Least Common Multiple of 400 and 405

LCM of 400 and 405 is 32400

Least common multiple can be found by multiplying the highest exponent prime factors of 400 and 405. First we will calculate the prime factors of 400 and 405.

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 405


3 405
3 135
3 45
3 15
5 5
1

Prime factors of 405 are 3,5. Prime factorization of 405 in exponential form is:

405 = 34×51

Now multiplying the highest exponent prime factors to calculate the LCM of 400 and 405.

LCM(400,405) = 24×34×52
LCM(400,405) = 32400

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 405

List of positive integer factors of 405 that divides 405 without a remainder.

1, 3, 5, 9, 15, 27, 45, 81, 135, 405

Least Common Multiple of 400 and 405 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 405, than apply into the LCM equation.

GCF(400,405) = 5
LCM(400,405) = ( 400 × 405) / 5
LCM(400,405) = 162000 / 5
LCM(400,405) = 32400

Properties of LCM 400 and 405

(i) The LCM of 405 and 400 is associative

LCM of 400 and 405 = LCM of 405 and 400

Related Least Common Multiples of 400

Related Least Common Multiples of 405

Frequently Asked Questions on LCM of 400 and 405

1. What is the LCM of 400 and 405?

Answer: LCM of 400 and 405 is 32400.

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 405?

Answer: Factors of 405 are 1, 3, 5, 9, 15, 27, 45, 81, 135, 405. There are 10 integers that are factors of 405. The greatest factor of 405 is 405.

4. How to Find the LCM of 400 and 405?

Answer:

Least Common Multiple of 400 and 405 = 32400

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 405

405 = 3 x 3 x 3 x 3 x 5

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

LCM = 32400 = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 5 x 5

Step 4: Therefore, the least common multiple of 400 and 405 is 32400.