Least Common Multiple of 408 and 414

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 414 the smallest integer that is 28152 that is divisible by both numbers.

Least Common Multiple (LCM) of 408 and 414 is 28152.

LCM(408,414) = 28152

LCM of 408 and 414

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

LCM of:
and

Least Common Multiple of 408 and 414

LCM of 408 and 414 is 28152

Least common multiple can be found by multiplying the highest exponent prime factors of 408 and 414. First we will calculate the prime factors of 408 and 414.

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 414


2 414
3 207
3 69
23 23
1

Prime factors of 414 are 2, 3,23. Prime factorization of 414 in exponential form is:

414 = 21×32×231

Now multiplying the highest exponent prime factors to calculate the LCM of 408 and 414.

LCM(408,414) = 23×32×171×231
LCM(408,414) = 28152

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 414

List of positive integer factors of 414 that divides 414 without a remainder.

1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414

Least Common Multiple of 408 and 414 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 414, than apply into the LCM equation.

GCF(408,414) = 6
LCM(408,414) = ( 408 × 414) / 6
LCM(408,414) = 168912 / 6
LCM(408,414) = 28152

Properties of LCM 408 and 414

(i) The LCM of 414 and 408 is associative

LCM of 408 and 414 = LCM of 414 and 408

Related Least Common Multiples of 408

Related Least Common Multiples of 414

Frequently Asked Questions on LCM of 408 and 414

1. What is the LCM of 408 and 414?

Answer: LCM of 408 and 414 is 28152.

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 414?

Answer: Factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414. There are 12 integers that are factors of 414. The greatest factor of 414 is 414.

4. How to Find the LCM of 408 and 414?

Answer:

Least Common Multiple of 408 and 414 = 28152

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 414

414 = 2 x 3 x 3 x 23

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

LCM = 28152 = 2 x 2 x 2 x 3 x 3 x 17 x 23

Step 4: Therefore, the least common multiple of 408 and 414 is 28152.