Least Common Multiple of 409 and 413

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 409 and 413 the smallest integer that is 168917 that is divisible by both numbers.

Least Common Multiple (LCM) of 409 and 413 is 168917.

LCM(409,413) = 168917

LCM of 409 and 413

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

LCM of:
and

Least Common Multiple of 409 and 413

LCM of 409 and 413 is 168917

Least common multiple can be found by multiplying the highest exponent prime factors of 409 and 413. First we will calculate the prime factors of 409 and 413.

Prime Factorization of 409


409 409
1

Prime factors of 409 are 409. Prime factorization of 409 in exponential form is:

409 = 4091

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

Now multiplying the highest exponent prime factors to calculate the LCM of 409 and 413.

LCM(409,413) = 71×591×4091
LCM(409,413) = 168917

Factors of 409

List of positive integer factors of 409 that divides 409 without a remainder.

1, 409

Factors of 413

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

1, 7, 59, 413

Least Common Multiple of 409 and 413 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 409 and 413, than apply into the LCM equation.

GCF(409,413) = 1
LCM(409,413) = ( 409 × 413) / 1
LCM(409,413) = 168917 / 1
LCM(409,413) = 168917

Properties of LCM 409 and 413

(i) The LCM of 413 and 409 is associative

LCM of 409 and 413 = LCM of 413 and 409

Related Least Common Multiples of 409

Related Least Common Multiples of 413

Frequently Asked Questions on LCM of 409 and 413

1. What is the LCM of 409 and 413?

Answer: LCM of 409 and 413 is 168917.

2. What are the Factors of 409?

Answer: Factors of 409 are 1, 409. There are 2 integers that are factors of 409. The greatest factor of 409 is 409.

3. 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.

4. How to Find the LCM of 409 and 413?

Answer:

Least Common Multiple of 409 and 413 = 168917

Step 1: Find the prime factorization of 409

409 = 409

Step 2: Find the prime factorization of 413

413 = 7 x 59

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

LCM = 168917 = 7 x 59 x 409

Step 4: Therefore, the least common multiple of 409 and 413 is 168917.