Least Common Multiple of 405 and 406

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 405 and 406 the smallest integer that is 164430 that is divisible by both numbers.

Least Common Multiple (LCM) of 405 and 406 is 164430.

LCM(405,406) = 164430

LCM of 405 and 406

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

LCM of:
and

Least Common Multiple of 405 and 406

LCM of 405 and 406 is 164430

Least common multiple can be found by multiplying the highest exponent prime factors of 405 and 406. First we will calculate the prime factors of 405 and 406.

Prime Factorization of 405


3 405
3 135
3 45
3 15
5 5
1

Prime factors of 405 are 3,5. Prime factorization of 405 in exponential form is:

405 = 34×51

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

Now multiplying the highest exponent prime factors to calculate the LCM of 405 and 406.

LCM(405,406) = 21×34×51×71×291
LCM(405,406) = 164430

Factors of 405

List of positive integer factors of 405 that divides 405 without a remainder.

1, 3, 5, 9, 15, 27, 45, 81, 135, 405

Factors of 406

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

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

Least Common Multiple of 405 and 406 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 405 and 406, than apply into the LCM equation.

GCF(405,406) = 1
LCM(405,406) = ( 405 × 406) / 1
LCM(405,406) = 164430 / 1
LCM(405,406) = 164430

Properties of LCM 405 and 406

(i) The LCM of 406 and 405 is associative

LCM of 405 and 406 = LCM of 406 and 405

Related Least Common Multiples of 405

Related Least Common Multiples of 406

Frequently Asked Questions on LCM of 405 and 406

1. What is the LCM of 405 and 406?

Answer: LCM of 405 and 406 is 164430.

2. What are the Factors of 405?

Answer: Factors of 405 are 1, 3, 5, 9, 15, 27, 45, 81, 135, 405. There are 10 integers that are factors of 405. The greatest factor of 405 is 405.

3. 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.

4. How to Find the LCM of 405 and 406?

Answer:

Least Common Multiple of 405 and 406 = 164430

Step 1: Find the prime factorization of 405

405 = 3 x 3 x 3 x 3 x 5

Step 2: Find the prime factorization of 406

406 = 2 x 7 x 29

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

LCM = 164430 = 2 x 3 x 3 x 3 x 3 x 5 x 7 x 29

Step 4: Therefore, the least common multiple of 405 and 406 is 164430.