Least Common Multiple of 409 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 409 and 416 the smallest integer that is 170144 that is divisible by both numbers.

Least Common Multiple (LCM) of 409 and 416 is 170144.

LCM(409,416) = 170144

LCM of 409 and 416

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

LCM of:
and

Least Common Multiple of 409 and 416

LCM of 409 and 416 is 170144

Least common multiple can be found by multiplying the highest exponent prime factors of 409 and 416. First we will calculate the prime factors of 409 and 416.

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 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 409 and 416.

LCM(409,416) = 25×131×4091
LCM(409,416) = 170144

Factors of 409

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

1, 409

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 409 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 409 and 416, than apply into the LCM equation.

GCF(409,416) = 1
LCM(409,416) = ( 409 × 416) / 1
LCM(409,416) = 170144 / 1
LCM(409,416) = 170144

Properties of LCM 409 and 416

(i) The LCM of 416 and 409 is associative

LCM of 409 and 416 = LCM of 416 and 409

Related Least Common Multiples of 409

Related Least Common Multiples of 416

Frequently Asked Questions on LCM of 409 and 416

1. What is the LCM of 409 and 416?

Answer: LCM of 409 and 416 is 170144.

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 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 409 and 416?

Answer:

Least Common Multiple of 409 and 416 = 170144

Step 1: Find the prime factorization of 409

409 = 409

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 = 170144 = 2 x 2 x 2 x 2 x 2 x 13 x 409

Step 4: Therefore, the least common multiple of 409 and 416 is 170144.