Least Common Multiple of 1404 and 1408

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 1408 the smallest integer that is 494208 that is divisible by both numbers.

Least Common Multiple (LCM) of 1404 and 1408 is 494208.

LCM(1404,1408) = 494208

LCM of 1404 and 1408

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

LCM of:
and

Least Common Multiple of 1404 and 1408

LCM of 1404 and 1408 is 494208

Least common multiple can be found by multiplying the highest exponent prime factors of 1404 and 1408. First we will calculate the prime factors of 1404 and 1408.

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 1408


2 1408
2 704
2 352
2 176
2 88
2 44
2 22
11 11
1

Prime factors of 1408 are 2,11. Prime factorization of 1408 in exponential form is:

1408 = 27×111

Now multiplying the highest exponent prime factors to calculate the LCM of 1404 and 1408.

LCM(1404,1408) = 27×33×111×131
LCM(1404,1408) = 494208

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 1408

List of positive integer factors of 1408 that divides 1408 without a remainder.

1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 128, 176, 352, 704, 1408

Least Common Multiple of 1404 and 1408 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 1408, than apply into the LCM equation.

GCF(1404,1408) = 4
LCM(1404,1408) = ( 1404 × 1408) / 4
LCM(1404,1408) = 1976832 / 4
LCM(1404,1408) = 494208

Properties of LCM 1404 and 1408

(i) The LCM of 1408 and 1404 is associative

LCM of 1404 and 1408 = LCM of 1408 and 1404

Related Least Common Multiples of 1404

Related Least Common Multiples of 1408

Frequently Asked Questions on LCM of 1404 and 1408

1. What is the LCM of 1404 and 1408?

Answer: LCM of 1404 and 1408 is 494208.

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 1408?

Answer: Factors of 1408 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 128, 176, 352, 704, 1408. There are 16 integers that are factors of 1408. The greatest factor of 1408 is 1408.

4. How to Find the LCM of 1404 and 1408?

Answer:

Least Common Multiple of 1404 and 1408 = 494208

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 1408

1408 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 11

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

LCM = 494208 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 11 x 13

Step 4: Therefore, the least common multiple of 1404 and 1408 is 494208.