Least Common Multiple of 392 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 392 and 400 the smallest integer that is 19600 that is divisible by both numbers.

Least Common Multiple (LCM) of 392 and 400 is 19600.

LCM(392,400) = 19600

LCM of 392 and 400

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

LCM of:
and

Least Common Multiple of 392 and 400

LCM of 392 and 400 is 19600

Least common multiple can be found by multiplying the highest exponent prime factors of 392 and 400. First we will calculate the prime factors of 392 and 400.

Prime Factorization of 392


2 392
2 196
2 98
7 49
7 7
1

Prime factors of 392 are 2,7. Prime factorization of 392 in exponential form is:

392 = 23×72

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 392 and 400.

LCM(392,400) = 24×52×72
LCM(392,400) = 19600

Factors of 392

List of positive integer factors of 392 that divides 392 without a remainder.

1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, 392

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 392 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 392 and 400, than apply into the LCM equation.

GCF(392,400) = 8
LCM(392,400) = ( 392 × 400) / 8
LCM(392,400) = 156800 / 8
LCM(392,400) = 19600

Properties of LCM 392 and 400

(i) The LCM of 400 and 392 is associative

LCM of 392 and 400 = LCM of 400 and 392

Related Least Common Multiples of 392

Related Least Common Multiples of 400

Frequently Asked Questions on LCM of 392 and 400

1. What is the LCM of 392 and 400?

Answer: LCM of 392 and 400 is 19600.

2. What are the Factors of 392?

Answer: Factors of 392 are 1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, 392. There are 12 integers that are factors of 392. The greatest factor of 392 is 392.

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 392 and 400?

Answer:

Least Common Multiple of 392 and 400 = 19600

Step 1: Find the prime factorization of 392

392 = 2 x 2 x 2 x 7 x 7

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 = 19600 = 2 x 2 x 2 x 2 x 5 x 5 x 7 x 7

Step 4: Therefore, the least common multiple of 392 and 400 is 19600.