Least Common Multiple of 1404 and 1410

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1404 and 1410 the smallest integer that is 329940 that is divisible by both numbers.

Least Common Multiple (LCM) of 1404 and 1410 is 329940.

LCM(1404,1410) = 329940

LCM of 1404 and 1410

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

LCM of:
and

Least Common Multiple of 1404 and 1410

LCM of 1404 and 1410 is 329940

Least common multiple can be found by multiplying the highest exponent prime factors of 1404 and 1410. First we will calculate the prime factors of 1404 and 1410.

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

Prime Factorization of 1410


2 1410
3 705
5 235
47 47
1

Prime factors of 1410 are 2, 3, 5,47. Prime factorization of 1410 in exponential form is:

1410 = 21×31×51×471

Now multiplying the highest exponent prime factors to calculate the LCM of 1404 and 1410.

LCM(1404,1410) = 22×33×51×131×471
LCM(1404,1410) = 329940

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

Factors of 1410

List of positive integer factors of 1410 that divides 1410 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 47, 94, 141, 235, 282, 470, 705, 1410

Least Common Multiple of 1404 and 1410 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1404 and 1410, than apply into the LCM equation.

GCF(1404,1410) = 6
LCM(1404,1410) = ( 1404 × 1410) / 6
LCM(1404,1410) = 1979640 / 6
LCM(1404,1410) = 329940

Properties of LCM 1404 and 1410

(i) The LCM of 1410 and 1404 is associative

LCM of 1404 and 1410 = LCM of 1410 and 1404

Related Least Common Multiples of 1404

Related Least Common Multiples of 1410

Frequently Asked Questions on LCM of 1404 and 1410

1. What is the LCM of 1404 and 1410?

Answer: LCM of 1404 and 1410 is 329940.

2. 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.

3. What are the Factors of 1410?

Answer: Factors of 1410 are 1, 2, 3, 5, 6, 10, 15, 30, 47, 94, 141, 235, 282, 470, 705, 1410. There are 16 integers that are factors of 1410. The greatest factor of 1410 is 1410.

4. How to Find the LCM of 1404 and 1410?

Answer:

Least Common Multiple of 1404 and 1410 = 329940

Step 1: Find the prime factorization of 1404

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

Step 2: Find the prime factorization of 1410

1410 = 2 x 3 x 5 x 47

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

LCM = 329940 = 2 x 2 x 3 x 3 x 3 x 5 x 13 x 47

Step 4: Therefore, the least common multiple of 1404 and 1410 is 329940.