Least Common Multiple of 413 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 413 and 416 the smallest integer that is 171808 that is divisible by both numbers.

Least Common Multiple (LCM) of 413 and 416 is 171808.

LCM(413,416) = 171808

LCM of 413 and 416

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

LCM of:
and

Least Common Multiple of 413 and 416

LCM of 413 and 416 is 171808

Least common multiple can be found by multiplying the highest exponent prime factors of 413 and 416. First we will calculate the prime factors of 413 and 416.

Prime Factorization of 413


7 413
59 59
1

Prime factors of 413 are 7,59. Prime factorization of 413 in exponential form is:

413 = 71×591

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 413 and 416.

LCM(413,416) = 25×71×131×591
LCM(413,416) = 171808

Factors of 413

List of positive integer factors of 413 that divides 413 without a remainder.

1, 7, 59, 413

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 413 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 413 and 416, than apply into the LCM equation.

GCF(413,416) = 1
LCM(413,416) = ( 413 × 416) / 1
LCM(413,416) = 171808 / 1
LCM(413,416) = 171808

Properties of LCM 413 and 416

(i) The LCM of 416 and 413 is associative

LCM of 413 and 416 = LCM of 416 and 413

Related Least Common Multiples of 413

Related Least Common Multiples of 416

Frequently Asked Questions on LCM of 413 and 416

1. What is the LCM of 413 and 416?

Answer: LCM of 413 and 416 is 171808.

2. What are the Factors of 413?

Answer: Factors of 413 are 1, 7, 59, 413. There are 4 integers that are factors of 413. The greatest factor of 413 is 413.

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 413 and 416?

Answer:

Least Common Multiple of 413 and 416 = 171808

Step 1: Find the prime factorization of 413

413 = 7 x 59

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 = 171808 = 2 x 2 x 2 x 2 x 2 x 7 x 13 x 59

Step 4: Therefore, the least common multiple of 413 and 416 is 171808.