Least Common Multiple of 409 and 414

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 414 the smallest integer that is 169326 that is divisible by both numbers.

Least Common Multiple (LCM) of 409 and 414 is 169326.

LCM(409,414) = 169326

LCM of 409 and 414

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

LCM of:
and

Least Common Multiple of 409 and 414

LCM of 409 and 414 is 169326

Least common multiple can be found by multiplying the highest exponent prime factors of 409 and 414. First we will calculate the prime factors of 409 and 414.

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 414


2 414
3 207
3 69
23 23
1

Prime factors of 414 are 2, 3,23. Prime factorization of 414 in exponential form is:

414 = 21×32×231

Now multiplying the highest exponent prime factors to calculate the LCM of 409 and 414.

LCM(409,414) = 21×32×231×4091
LCM(409,414) = 169326

Factors of 409

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

1, 409

Factors of 414

List of positive integer factors of 414 that divides 414 without a remainder.

1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414

Least Common Multiple of 409 and 414 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 414, than apply into the LCM equation.

GCF(409,414) = 1
LCM(409,414) = ( 409 × 414) / 1
LCM(409,414) = 169326 / 1
LCM(409,414) = 169326

Properties of LCM 409 and 414

(i) The LCM of 414 and 409 is associative

LCM of 409 and 414 = LCM of 414 and 409

Related Least Common Multiples of 409

Related Least Common Multiples of 414

Frequently Asked Questions on LCM of 409 and 414

1. What is the LCM of 409 and 414?

Answer: LCM of 409 and 414 is 169326.

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 414?

Answer: Factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414. There are 12 integers that are factors of 414. The greatest factor of 414 is 414.

4. How to Find the LCM of 409 and 414?

Answer:

Least Common Multiple of 409 and 414 = 169326

Step 1: Find the prime factorization of 409

409 = 409

Step 2: Find the prime factorization of 414

414 = 2 x 3 x 3 x 23

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

LCM = 169326 = 2 x 3 x 3 x 23 x 409

Step 4: Therefore, the least common multiple of 409 and 414 is 169326.