Least Common Multiple of 409 and 417

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 417 the smallest integer that is 170553 that is divisible by both numbers.

Least Common Multiple (LCM) of 409 and 417 is 170553.

LCM(409,417) = 170553

LCM of 409 and 417

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

LCM of:
and

Least Common Multiple of 409 and 417

LCM of 409 and 417 is 170553

Least common multiple can be found by multiplying the highest exponent prime factors of 409 and 417. First we will calculate the prime factors of 409 and 417.

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 417


3 417
139 139
1

Prime factors of 417 are 3,139. Prime factorization of 417 in exponential form is:

417 = 31×1391

Now multiplying the highest exponent prime factors to calculate the LCM of 409 and 417.

LCM(409,417) = 31×1391×4091
LCM(409,417) = 170553

Factors of 409

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

1, 409

Factors of 417

List of positive integer factors of 417 that divides 417 without a remainder.

1, 3, 139, 417

Least Common Multiple of 409 and 417 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 417, than apply into the LCM equation.

GCF(409,417) = 1
LCM(409,417) = ( 409 × 417) / 1
LCM(409,417) = 170553 / 1
LCM(409,417) = 170553

Properties of LCM 409 and 417

(i) The LCM of 417 and 409 is associative

LCM of 409 and 417 = LCM of 417 and 409

Related Least Common Multiples of 409

Related Least Common Multiples of 417

Frequently Asked Questions on LCM of 409 and 417

1. What is the LCM of 409 and 417?

Answer: LCM of 409 and 417 is 170553.

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 417?

Answer: Factors of 417 are 1, 3, 139, 417. There are 4 integers that are factors of 417. The greatest factor of 417 is 417.

4. How to Find the LCM of 409 and 417?

Answer:

Least Common Multiple of 409 and 417 = 170553

Step 1: Find the prime factorization of 409

409 = 409

Step 2: Find the prime factorization of 417

417 = 3 x 139

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

LCM = 170553 = 3 x 139 x 409

Step 4: Therefore, the least common multiple of 409 and 417 is 170553.