Least Common Multiple of 1400 and 1404

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1400 and 1404 the smallest integer that is 491400 that is divisible by both numbers.

Least Common Multiple (LCM) of 1400 and 1404 is 491400.

LCM(1400,1404) = 491400

LCM of 1400 and 1404

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

LCM of:
and

Least Common Multiple of 1400 and 1404

LCM of 1400 and 1404 is 491400

Least common multiple can be found by multiplying the highest exponent prime factors of 1400 and 1404. First we will calculate the prime factors of 1400 and 1404.

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

Prime Factorization of 1404


2 1404
2 702
3 351
3 117
3 39
13 13
1

Prime factors of 1404 are 2, 3,13. Prime factorization of 1404 in exponential form is:

1404 = 22×33×131

Now multiplying the highest exponent prime factors to calculate the LCM of 1400 and 1404.

LCM(1400,1404) = 23×33×52×71×131
LCM(1400,1404) = 491400

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

Factors of 1404

List of positive integer factors of 1404 that divides 1404 without a remainder.

1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 27, 36, 39, 52, 54, 78, 108, 117, 156, 234, 351, 468, 702, 1404

Least Common Multiple of 1400 and 1404 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1400 and 1404, than apply into the LCM equation.

GCF(1400,1404) = 4
LCM(1400,1404) = ( 1400 × 1404) / 4
LCM(1400,1404) = 1965600 / 4
LCM(1400,1404) = 491400

Properties of LCM 1400 and 1404

(i) The LCM of 1404 and 1400 is associative

LCM of 1400 and 1404 = LCM of 1404 and 1400

Related Least Common Multiples of 1400

Related Least Common Multiples of 1404

Frequently Asked Questions on LCM of 1400 and 1404

1. What is the LCM of 1400 and 1404?

Answer: LCM of 1400 and 1404 is 491400.

2. 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.

3. What are the Factors of 1404?

Answer: Factors of 1404 are 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 27, 36, 39, 52, 54, 78, 108, 117, 156, 234, 351, 468, 702, 1404. There are 24 integers that are factors of 1404. The greatest factor of 1404 is 1404.

4. How to Find the LCM of 1400 and 1404?

Answer:

Least Common Multiple of 1400 and 1404 = 491400

Step 1: Find the prime factorization of 1400

1400 = 2 x 2 x 2 x 5 x 5 x 7

Step 2: Find the prime factorization of 1404

1404 = 2 x 2 x 3 x 3 x 3 x 13

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

LCM = 491400 = 2 x 2 x 2 x 3 x 3 x 3 x 5 x 5 x 7 x 13

Step 4: Therefore, the least common multiple of 1400 and 1404 is 491400.