Least Common Multiple of 409 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 409 and 410 the smallest integer that is 167690 that is divisible by both numbers.

Least Common Multiple (LCM) of 409 and 410 is 167690.

LCM(409,410) = 167690

LCM of 409 and 410

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

LCM of:
and

Least Common Multiple of 409 and 410

LCM of 409 and 410 is 167690

Least common multiple can be found by multiplying the highest exponent prime factors of 409 and 410. First we will calculate the prime factors of 409 and 410.

Prime Factorization of 409


409 409
1

Prime factors of 409 are 409. Prime factorization of 409 in exponential form is:

409 = 4091

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 409 and 410.

LCM(409,410) = 21×51×411×4091
LCM(409,410) = 167690

Factors of 409

List of positive integer factors of 409 that divides 409 without a remainder.

1, 409

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 409 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 409 and 410, than apply into the LCM equation.

GCF(409,410) = 1
LCM(409,410) = ( 409 × 410) / 1
LCM(409,410) = 167690 / 1
LCM(409,410) = 167690

Properties of LCM 409 and 410

(i) The LCM of 410 and 409 is associative

LCM of 409 and 410 = LCM of 410 and 409

Related Least Common Multiples of 409

Related Least Common Multiples of 410

Frequently Asked Questions on LCM of 409 and 410

1. What is the LCM of 409 and 410?

Answer: LCM of 409 and 410 is 167690.

2. What are the Factors of 409?

Answer: Factors of 409 are 1, 409. There are 2 integers that are factors of 409. The greatest factor of 409 is 409.

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 409 and 410?

Answer:

Least Common Multiple of 409 and 410 = 167690

Step 1: Find the prime factorization of 409

409 = 409

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 = 167690 = 2 x 5 x 41 x 409

Step 4: Therefore, the least common multiple of 409 and 410 is 167690.