Least Common Multiple of 409 and 415

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 415 the smallest integer that is 169735 that is divisible by both numbers.

Least Common Multiple (LCM) of 409 and 415 is 169735.

LCM(409,415) = 169735

LCM of 409 and 415

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

LCM of:
and

Least Common Multiple of 409 and 415

LCM of 409 and 415 is 169735

Least common multiple can be found by multiplying the highest exponent prime factors of 409 and 415. First we will calculate the prime factors of 409 and 415.

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 415


5 415
83 83
1

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

415 = 51×831

Now multiplying the highest exponent prime factors to calculate the LCM of 409 and 415.

LCM(409,415) = 51×831×4091
LCM(409,415) = 169735

Factors of 409

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

1, 409

Factors of 415

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

1, 5, 83, 415

Least Common Multiple of 409 and 415 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 415, than apply into the LCM equation.

GCF(409,415) = 1
LCM(409,415) = ( 409 × 415) / 1
LCM(409,415) = 169735 / 1
LCM(409,415) = 169735

Properties of LCM 409 and 415

(i) The LCM of 415 and 409 is associative

LCM of 409 and 415 = LCM of 415 and 409

Related Least Common Multiples of 409

Related Least Common Multiples of 415

Frequently Asked Questions on LCM of 409 and 415

1. What is the LCM of 409 and 415?

Answer: LCM of 409 and 415 is 169735.

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 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.

4. How to Find the LCM of 409 and 415?

Answer:

Least Common Multiple of 409 and 415 = 169735

Step 1: Find the prime factorization of 409

409 = 409

Step 2: Find the prime factorization of 415

415 = 5 x 83

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

LCM = 169735 = 5 x 83 x 409

Step 4: Therefore, the least common multiple of 409 and 415 is 169735.