Least Common Multiple of 408 and 415

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 408 and 415 the smallest integer that is 169320 that is divisible by both numbers.

Least Common Multiple (LCM) of 408 and 415 is 169320.

LCM(408,415) = 169320

LCM of 408 and 415

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

LCM of:
and

Least Common Multiple of 408 and 415

LCM of 408 and 415 is 169320

Least common multiple can be found by multiplying the highest exponent prime factors of 408 and 415. First we will calculate the prime factors of 408 and 415.

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

Prime Factorization of 415


5 415
83 83
1

Prime factors of 415 are 5,83. Prime factorization of 415 in exponential form is:

415 = 51×831

Now multiplying the highest exponent prime factors to calculate the LCM of 408 and 415.

LCM(408,415) = 23×31×51×171×831
LCM(408,415) = 169320

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

Factors of 415

List of positive integer factors of 415 that divides 415 without a remainder.

1, 5, 83, 415

Least Common Multiple of 408 and 415 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 408 and 415, than apply into the LCM equation.

GCF(408,415) = 1
LCM(408,415) = ( 408 × 415) / 1
LCM(408,415) = 169320 / 1
LCM(408,415) = 169320

Properties of LCM 408 and 415

(i) The LCM of 415 and 408 is associative

LCM of 408 and 415 = LCM of 415 and 408

Related Least Common Multiples of 408

Related Least Common Multiples of 415

Frequently Asked Questions on LCM of 408 and 415

1. What is the LCM of 408 and 415?

Answer: LCM of 408 and 415 is 169320.

2. 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.

3. What are the Factors of 415?

Answer: Factors of 415 are 1, 5, 83, 415. There are 4 integers that are factors of 415. The greatest factor of 415 is 415.

4. How to Find the LCM of 408 and 415?

Answer:

Least Common Multiple of 408 and 415 = 169320

Step 1: Find the prime factorization of 408

408 = 2 x 2 x 2 x 3 x 17

Step 2: Find the prime factorization of 415

415 = 5 x 83

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

LCM = 169320 = 2 x 2 x 2 x 3 x 5 x 17 x 83

Step 4: Therefore, the least common multiple of 408 and 415 is 169320.