Least Common Multiple of 408 and 413

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 413 the smallest integer that is 168504 that is divisible by both numbers.

Least Common Multiple (LCM) of 408 and 413 is 168504.

LCM(408,413) = 168504

LCM of 408 and 413

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

LCM of:
and

Least Common Multiple of 408 and 413

LCM of 408 and 413 is 168504

Least common multiple can be found by multiplying the highest exponent prime factors of 408 and 413. First we will calculate the prime factors of 408 and 413.

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 413


7 413
59 59
1

Prime factors of 413 are 7,59. Prime factorization of 413 in exponential form is:

413 = 71×591

Now multiplying the highest exponent prime factors to calculate the LCM of 408 and 413.

LCM(408,413) = 23×31×71×171×591
LCM(408,413) = 168504

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 413

List of positive integer factors of 413 that divides 413 without a remainder.

1, 7, 59, 413

Least Common Multiple of 408 and 413 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 413, than apply into the LCM equation.

GCF(408,413) = 1
LCM(408,413) = ( 408 × 413) / 1
LCM(408,413) = 168504 / 1
LCM(408,413) = 168504

Properties of LCM 408 and 413

(i) The LCM of 413 and 408 is associative

LCM of 408 and 413 = LCM of 413 and 408

Related Least Common Multiples of 408

Related Least Common Multiples of 413

Frequently Asked Questions on LCM of 408 and 413

1. What is the LCM of 408 and 413?

Answer: LCM of 408 and 413 is 168504.

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 413?

Answer: Factors of 413 are 1, 7, 59, 413. There are 4 integers that are factors of 413. The greatest factor of 413 is 413.

4. How to Find the LCM of 408 and 413?

Answer:

Least Common Multiple of 408 and 413 = 168504

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 413

413 = 7 x 59

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

LCM = 168504 = 2 x 2 x 2 x 3 x 7 x 17 x 59

Step 4: Therefore, the least common multiple of 408 and 413 is 168504.