Least Common Multiple of 415 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 415 and 416 the smallest integer that is 172640 that is divisible by both numbers.

Least Common Multiple (LCM) of 415 and 416 is 172640.

LCM(415,416) = 172640

LCM of 415 and 416

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

LCM of:
and

Least Common Multiple of 415 and 416

LCM of 415 and 416 is 172640

Least common multiple can be found by multiplying the highest exponent prime factors of 415 and 416. First we will calculate the prime factors of 415 and 416.

Prime Factorization of 415


5 415
83 83
1

Prime factors of 415 are 5,83. Prime factorization of 415 in exponential form is:

415 = 51×831

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 415 and 416.

LCM(415,416) = 25×51×131×831
LCM(415,416) = 172640

Factors of 415

List of positive integer factors of 415 that divides 415 without a remainder.

1, 5, 83, 415

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 415 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 415 and 416, than apply into the LCM equation.

GCF(415,416) = 1
LCM(415,416) = ( 415 × 416) / 1
LCM(415,416) = 172640 / 1
LCM(415,416) = 172640

Properties of LCM 415 and 416

(i) The LCM of 416 and 415 is associative

LCM of 415 and 416 = LCM of 416 and 415

Related Least Common Multiples of 415

Related Least Common Multiples of 416

Frequently Asked Questions on LCM of 415 and 416

1. What is the LCM of 415 and 416?

Answer: LCM of 415 and 416 is 172640.

2. What are the Factors of 415?

Answer: Factors of 415 are 1, 5, 83, 415. There are 4 integers that are factors of 415. The greatest factor of 415 is 415.

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 415 and 416?

Answer:

Least Common Multiple of 415 and 416 = 172640

Step 1: Find the prime factorization of 415

415 = 5 x 83

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 = 172640 = 2 x 2 x 2 x 2 x 2 x 5 x 13 x 83

Step 4: Therefore, the least common multiple of 415 and 416 is 172640.