Least Common Multiple of 405 and 408

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 405 and 408 the smallest integer that is 55080 that is divisible by both numbers.

Least Common Multiple (LCM) of 405 and 408 is 55080.

LCM(405,408) = 55080

LCM of 405 and 408

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

LCM of:
and

Least Common Multiple of 405 and 408

LCM of 405 and 408 is 55080

Least common multiple can be found by multiplying the highest exponent prime factors of 405 and 408. First we will calculate the prime factors of 405 and 408.

Prime Factorization of 405


3 405
3 135
3 45
3 15
5 5
1

Prime factors of 405 are 3,5. Prime factorization of 405 in exponential form is:

405 = 34×51

Prime Factorization of 408


2 408
2 204
2 102
3 51
17 17
1

Prime factors of 408 are 2, 3,17. Prime factorization of 408 in exponential form is:

408 = 23×31×171

Now multiplying the highest exponent prime factors to calculate the LCM of 405 and 408.

LCM(405,408) = 23×34×51×171
LCM(405,408) = 55080

Factors of 405

List of positive integer factors of 405 that divides 405 without a remainder.

1, 3, 5, 9, 15, 27, 45, 81, 135, 405

Factors of 408

List of positive integer factors of 408 that divides 408 without a remainder.

1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408

Least Common Multiple of 405 and 408 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 405 and 408, than apply into the LCM equation.

GCF(405,408) = 3
LCM(405,408) = ( 405 × 408) / 3
LCM(405,408) = 165240 / 3
LCM(405,408) = 55080

Properties of LCM 405 and 408

(i) The LCM of 408 and 405 is associative

LCM of 405 and 408 = LCM of 408 and 405

Related Least Common Multiples of 405

Related Least Common Multiples of 408

Frequently Asked Questions on LCM of 405 and 408

1. What is the LCM of 405 and 408?

Answer: LCM of 405 and 408 is 55080.

2. What are the Factors of 405?

Answer: Factors of 405 are 1, 3, 5, 9, 15, 27, 45, 81, 135, 405. There are 10 integers that are factors of 405. The greatest factor of 405 is 405.

3. What are the Factors of 408?

Answer: Factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408. There are 16 integers that are factors of 408. The greatest factor of 408 is 408.

4. How to Find the LCM of 405 and 408?

Answer:

Least Common Multiple of 405 and 408 = 55080

Step 1: Find the prime factorization of 405

405 = 3 x 3 x 3 x 3 x 5

Step 2: Find the prime factorization of 408

408 = 2 x 2 x 2 x 3 x 17

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

LCM = 55080 = 2 x 2 x 2 x 3 x 3 x 3 x 3 x 5 x 17

Step 4: Therefore, the least common multiple of 405 and 408 is 55080.