Least Common Multiple of 399 and 400

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 399 and 400 the smallest integer that is 159600 that is divisible by both numbers.

Least Common Multiple (LCM) of 399 and 400 is 159600.

LCM(399,400) = 159600

LCM of 399 and 400

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

LCM of:
and

Least Common Multiple of 399 and 400

LCM of 399 and 400 is 159600

Least common multiple can be found by multiplying the highest exponent prime factors of 399 and 400. First we will calculate the prime factors of 399 and 400.

Prime Factorization of 399


3 399
7 133
19 19
1

Prime factors of 399 are 3, 7,19. Prime factorization of 399 in exponential form is:

399 = 31×71×191

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

Now multiplying the highest exponent prime factors to calculate the LCM of 399 and 400.

LCM(399,400) = 24×31×52×71×191
LCM(399,400) = 159600

Factors of 399

List of positive integer factors of 399 that divides 399 without a remainder.

1, 3, 7, 19, 21, 57, 133, 399

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

Least Common Multiple of 399 and 400 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 399 and 400, than apply into the LCM equation.

GCF(399,400) = 1
LCM(399,400) = ( 399 × 400) / 1
LCM(399,400) = 159600 / 1
LCM(399,400) = 159600

Properties of LCM 399 and 400

(i) The LCM of 400 and 399 is associative

LCM of 399 and 400 = LCM of 400 and 399

Related Least Common Multiples of 399

Related Least Common Multiples of 400

Frequently Asked Questions on LCM of 399 and 400

1. What is the LCM of 399 and 400?

Answer: LCM of 399 and 400 is 159600.

2. What are the Factors of 399?

Answer: Factors of 399 are 1, 3, 7, 19, 21, 57, 133, 399. There are 8 integers that are factors of 399. The greatest factor of 399 is 399.

3. 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.

4. How to Find the LCM of 399 and 400?

Answer:

Least Common Multiple of 399 and 400 = 159600

Step 1: Find the prime factorization of 399

399 = 3 x 7 x 19

Step 2: Find the prime factorization of 400

400 = 2 x 2 x 2 x 2 x 5 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 = 159600 = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 7 x 19

Step 4: Therefore, the least common multiple of 399 and 400 is 159600.