Least Common Multiple of 1392 and 1400

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1392 and 1400 the smallest integer that is 243600 that is divisible by both numbers.

Least Common Multiple (LCM) of 1392 and 1400 is 243600.

LCM(1392,1400) = 243600

LCM of 1392 and 1400

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

LCM of:
and

Least Common Multiple of 1392 and 1400

LCM of 1392 and 1400 is 243600

Least common multiple can be found by multiplying the highest exponent prime factors of 1392 and 1400. First we will calculate the prime factors of 1392 and 1400.

Prime Factorization of 1392


2 1392
2 696
2 348
2 174
3 87
29 29
1

Prime factors of 1392 are 2, 3,29. Prime factorization of 1392 in exponential form is:

1392 = 24×31×291

Prime Factorization of 1400


2 1400
2 700
2 350
5 175
5 35
7 7
1

Prime factors of 1400 are 2, 5,7. Prime factorization of 1400 in exponential form is:

1400 = 23×52×71

Now multiplying the highest exponent prime factors to calculate the LCM of 1392 and 1400.

LCM(1392,1400) = 24×31×52×71×291
LCM(1392,1400) = 243600

Factors of 1392

List of positive integer factors of 1392 that divides 1392 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 29, 48, 58, 87, 116, 174, 232, 348, 464, 696, 1392

Factors of 1400

List of positive integer factors of 1400 that divides 1400 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 350, 700, 1400

Least Common Multiple of 1392 and 1400 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1392 and 1400, than apply into the LCM equation.

GCF(1392,1400) = 8
LCM(1392,1400) = ( 1392 × 1400) / 8
LCM(1392,1400) = 1948800 / 8
LCM(1392,1400) = 243600

Properties of LCM 1392 and 1400

(i) The LCM of 1400 and 1392 is associative

LCM of 1392 and 1400 = LCM of 1400 and 1392

Related Least Common Multiples of 1392

Related Least Common Multiples of 1400

Frequently Asked Questions on LCM of 1392 and 1400

1. What is the LCM of 1392 and 1400?

Answer: LCM of 1392 and 1400 is 243600.

2. What are the Factors of 1392?

Answer: Factors of 1392 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 29, 48, 58, 87, 116, 174, 232, 348, 464, 696, 1392. There are 20 integers that are factors of 1392. The greatest factor of 1392 is 1392.

3. What are the Factors of 1400?

Answer: Factors of 1400 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 350, 700, 1400. There are 24 integers that are factors of 1400. The greatest factor of 1400 is 1400.

4. How to Find the LCM of 1392 and 1400?

Answer:

Least Common Multiple of 1392 and 1400 = 243600

Step 1: Find the prime factorization of 1392

1392 = 2 x 2 x 2 x 2 x 3 x 29

Step 2: Find the prime factorization of 1400

1400 = 2 x 2 x 2 x 5 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 = 243600 = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 7 x 29

Step 4: Therefore, the least common multiple of 1392 and 1400 is 243600.