Least Common Multiple of 408 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 408 and 412 the smallest integer that is 42024 that is divisible by both numbers.

Least Common Multiple (LCM) of 408 and 412 is 42024.

LCM(408,412) = 42024

LCM of 408 and 412

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

LCM of:
and

Least Common Multiple of 408 and 412

LCM of 408 and 412 is 42024

Least common multiple can be found by multiplying the highest exponent prime factors of 408 and 412. First we will calculate the prime factors of 408 and 412.

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 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 408 and 412.

LCM(408,412) = 23×31×171×1031
LCM(408,412) = 42024

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 412

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

1, 2, 4, 103, 206, 412

Least Common Multiple of 408 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 408 and 412, than apply into the LCM equation.

GCF(408,412) = 4
LCM(408,412) = ( 408 × 412) / 4
LCM(408,412) = 168096 / 4
LCM(408,412) = 42024

Properties of LCM 408 and 412

(i) The LCM of 412 and 408 is associative

LCM of 408 and 412 = LCM of 412 and 408

Related Least Common Multiples of 408

Related Least Common Multiples of 412

Frequently Asked Questions on LCM of 408 and 412

1. What is the LCM of 408 and 412?

Answer: LCM of 408 and 412 is 42024.

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 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 408 and 412?

Answer:

Least Common Multiple of 408 and 412 = 42024

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 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 = 42024 = 2 x 2 x 2 x 3 x 17 x 103

Step 4: Therefore, the least common multiple of 408 and 412 is 42024.