Least Common Multiple of 409 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 409 and 412 the smallest integer that is 168508 that is divisible by both numbers.

Least Common Multiple (LCM) of 409 and 412 is 168508.

LCM(409,412) = 168508

LCM of 409 and 412

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

LCM of:
and

Least Common Multiple of 409 and 412

LCM of 409 and 412 is 168508

Least common multiple can be found by multiplying the highest exponent prime factors of 409 and 412. First we will calculate the prime factors of 409 and 412.

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 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 409 and 412.

LCM(409,412) = 22×1031×4091
LCM(409,412) = 168508

Factors of 409

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

1, 409

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 409 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 409 and 412, than apply into the LCM equation.

GCF(409,412) = 1
LCM(409,412) = ( 409 × 412) / 1
LCM(409,412) = 168508 / 1
LCM(409,412) = 168508

Properties of LCM 409 and 412

(i) The LCM of 412 and 409 is associative

LCM of 409 and 412 = LCM of 412 and 409

Related Least Common Multiples of 409

Related Least Common Multiples of 412

Frequently Asked Questions on LCM of 409 and 412

1. What is the LCM of 409 and 412?

Answer: LCM of 409 and 412 is 168508.

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 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 409 and 412?

Answer:

Least Common Multiple of 409 and 412 = 168508

Step 1: Find the prime factorization of 409

409 = 409

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 = 168508 = 2 x 2 x 103 x 409

Step 4: Therefore, the least common multiple of 409 and 412 is 168508.