Least Common Multiple of 408 and 416

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 416 the smallest integer that is 21216 that is divisible by both numbers.

Least Common Multiple (LCM) of 408 and 416 is 21216.

LCM(408,416) = 21216

LCM of 408 and 416

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

LCM of:
and

Least Common Multiple of 408 and 416

LCM of 408 and 416 is 21216

Least common multiple can be found by multiplying the highest exponent prime factors of 408 and 416. First we will calculate the prime factors of 408 and 416.

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 416


2 416
2 208
2 104
2 52
2 26
13 13
1

Prime factors of 416 are 2,13. Prime factorization of 416 in exponential form is:

416 = 25×131

Now multiplying the highest exponent prime factors to calculate the LCM of 408 and 416.

LCM(408,416) = 25×31×131×171
LCM(408,416) = 21216

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 416

List of positive integer factors of 416 that divides 416 without a remainder.

1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416

Least Common Multiple of 408 and 416 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 416, than apply into the LCM equation.

GCF(408,416) = 8
LCM(408,416) = ( 408 × 416) / 8
LCM(408,416) = 169728 / 8
LCM(408,416) = 21216

Properties of LCM 408 and 416

(i) The LCM of 416 and 408 is associative

LCM of 408 and 416 = LCM of 416 and 408

Related Least Common Multiples of 408

Related Least Common Multiples of 416

Frequently Asked Questions on LCM of 408 and 416

1. What is the LCM of 408 and 416?

Answer: LCM of 408 and 416 is 21216.

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 416?

Answer: Factors of 416 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416. There are 12 integers that are factors of 416. The greatest factor of 416 is 416.

4. How to Find the LCM of 408 and 416?

Answer:

Least Common Multiple of 408 and 416 = 21216

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 416

416 = 2 x 2 x 2 x 2 x 2 x 13

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

LCM = 21216 = 2 x 2 x 2 x 2 x 2 x 3 x 13 x 17

Step 4: Therefore, the least common multiple of 408 and 416 is 21216.