Least Common Multiple of 406 and 409

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 406 and 409 the smallest integer that is 166054 that is divisible by both numbers.

Least Common Multiple (LCM) of 406 and 409 is 166054.

LCM(406,409) = 166054

LCM of 406 and 409

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

LCM of:
and

Least Common Multiple of 406 and 409

LCM of 406 and 409 is 166054

Least common multiple can be found by multiplying the highest exponent prime factors of 406 and 409. First we will calculate the prime factors of 406 and 409.

Prime Factorization of 406


2 406
7 203
29 29
1

Prime factors of 406 are 2, 7,29. Prime factorization of 406 in exponential form is:

406 = 21×71×291

Prime Factorization of 409


409 409
1

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

409 = 4091

Now multiplying the highest exponent prime factors to calculate the LCM of 406 and 409.

LCM(406,409) = 21×71×291×4091
LCM(406,409) = 166054

Factors of 406

List of positive integer factors of 406 that divides 406 without a remainder.

1, 2, 7, 14, 29, 58, 203, 406

Factors of 409

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

1, 409

Least Common Multiple of 406 and 409 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 406 and 409, than apply into the LCM equation.

GCF(406,409) = 1
LCM(406,409) = ( 406 × 409) / 1
LCM(406,409) = 166054 / 1
LCM(406,409) = 166054

Properties of LCM 406 and 409

(i) The LCM of 409 and 406 is associative

LCM of 406 and 409 = LCM of 409 and 406

Related Least Common Multiples of 406

Related Least Common Multiples of 409

Frequently Asked Questions on LCM of 406 and 409

1. What is the LCM of 406 and 409?

Answer: LCM of 406 and 409 is 166054.

2. What are the Factors of 406?

Answer: Factors of 406 are 1, 2, 7, 14, 29, 58, 203, 406. There are 8 integers that are factors of 406. The greatest factor of 406 is 406.

3. 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.

4. How to Find the LCM of 406 and 409?

Answer:

Least Common Multiple of 406 and 409 = 166054

Step 1: Find the prime factorization of 406

406 = 2 x 7 x 29

Step 2: Find the prime factorization of 409

409 = 409

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

LCM = 166054 = 2 x 7 x 29 x 409

Step 4: Therefore, the least common multiple of 406 and 409 is 166054.