Least Common Multiple of 408 and 410

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 410 the smallest integer that is 83640 that is divisible by both numbers.

Least Common Multiple (LCM) of 408 and 410 is 83640.

LCM(408,410) = 83640

LCM of 408 and 410

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

LCM of:
and

Least Common Multiple of 408 and 410

LCM of 408 and 410 is 83640

Least common multiple can be found by multiplying the highest exponent prime factors of 408 and 410. First we will calculate the prime factors of 408 and 410.

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 410


2 410
5 205
41 41
1

Prime factors of 410 are 2, 5,41. Prime factorization of 410 in exponential form is:

410 = 21×51×411

Now multiplying the highest exponent prime factors to calculate the LCM of 408 and 410.

LCM(408,410) = 23×31×51×171×411
LCM(408,410) = 83640

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 410

List of positive integer factors of 410 that divides 410 without a remainder.

1, 2, 5, 10, 41, 82, 205, 410

Least Common Multiple of 408 and 410 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 410, than apply into the LCM equation.

GCF(408,410) = 2
LCM(408,410) = ( 408 × 410) / 2
LCM(408,410) = 167280 / 2
LCM(408,410) = 83640

Properties of LCM 408 and 410

(i) The LCM of 410 and 408 is associative

LCM of 408 and 410 = LCM of 410 and 408

Related Least Common Multiples of 408

Related Least Common Multiples of 410

Frequently Asked Questions on LCM of 408 and 410

1. What is the LCM of 408 and 410?

Answer: LCM of 408 and 410 is 83640.

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 410?

Answer: Factors of 410 are 1, 2, 5, 10, 41, 82, 205, 410. There are 8 integers that are factors of 410. The greatest factor of 410 is 410.

4. How to Find the LCM of 408 and 410?

Answer:

Least Common Multiple of 408 and 410 = 83640

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 410

410 = 2 x 5 x 41

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

LCM = 83640 = 2 x 2 x 2 x 3 x 5 x 17 x 41

Step 4: Therefore, the least common multiple of 408 and 410 is 83640.