Least Common Multiple of 405 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 405 and 410 the smallest integer that is 33210 that is divisible by both numbers.

Least Common Multiple (LCM) of 405 and 410 is 33210.

LCM(405,410) = 33210

LCM of 405 and 410

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

LCM of:
and

Least Common Multiple of 405 and 410

LCM of 405 and 410 is 33210

Least common multiple can be found by multiplying the highest exponent prime factors of 405 and 410. First we will calculate the prime factors of 405 and 410.

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 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 405 and 410.

LCM(405,410) = 21×34×51×411
LCM(405,410) = 33210

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 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 405 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 405 and 410, than apply into the LCM equation.

GCF(405,410) = 5
LCM(405,410) = ( 405 × 410) / 5
LCM(405,410) = 166050 / 5
LCM(405,410) = 33210

Properties of LCM 405 and 410

(i) The LCM of 410 and 405 is associative

LCM of 405 and 410 = LCM of 410 and 405

Related Least Common Multiples of 405

Related Least Common Multiples of 410

Frequently Asked Questions on LCM of 405 and 410

1. What is the LCM of 405 and 410?

Answer: LCM of 405 and 410 is 33210.

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 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 405 and 410?

Answer:

Least Common Multiple of 405 and 410 = 33210

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 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 = 33210 = 2 x 3 x 3 x 3 x 3 x 5 x 41

Step 4: Therefore, the least common multiple of 405 and 410 is 33210.