Least Common Multiple of 405 and 412

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 412 the smallest integer that is 166860 that is divisible by both numbers.

Least Common Multiple (LCM) of 405 and 412 is 166860.

LCM(405,412) = 166860

LCM of 405 and 412

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

LCM of:
and

Least Common Multiple of 405 and 412

LCM of 405 and 412 is 166860

Least common multiple can be found by multiplying the highest exponent prime factors of 405 and 412. First we will calculate the prime factors of 405 and 412.

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 412


2 412
2 206
103 103
1

Prime factors of 412 are 2,103. Prime factorization of 412 in exponential form is:

412 = 22×1031

Now multiplying the highest exponent prime factors to calculate the LCM of 405 and 412.

LCM(405,412) = 22×34×51×1031
LCM(405,412) = 166860

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 412

List of positive integer factors of 412 that divides 412 without a remainder.

1, 2, 4, 103, 206, 412

Least Common Multiple of 405 and 412 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 412, than apply into the LCM equation.

GCF(405,412) = 1
LCM(405,412) = ( 405 × 412) / 1
LCM(405,412) = 166860 / 1
LCM(405,412) = 166860

Properties of LCM 405 and 412

(i) The LCM of 412 and 405 is associative

LCM of 405 and 412 = LCM of 412 and 405

Related Least Common Multiples of 405

Related Least Common Multiples of 412

Frequently Asked Questions on LCM of 405 and 412

1. What is the LCM of 405 and 412?

Answer: LCM of 405 and 412 is 166860.

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 412?

Answer: Factors of 412 are 1, 2, 4, 103, 206, 412. There are 6 integers that are factors of 412. The greatest factor of 412 is 412.

4. How to Find the LCM of 405 and 412?

Answer:

Least Common Multiple of 405 and 412 = 166860

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 412

412 = 2 x 2 x 103

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

LCM = 166860 = 2 x 2 x 3 x 3 x 3 x 3 x 5 x 103

Step 4: Therefore, the least common multiple of 405 and 412 is 166860.