Least Common Multiple of 405 and 407

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 407 the smallest integer that is 164835 that is divisible by both numbers.

Least Common Multiple (LCM) of 405 and 407 is 164835.

LCM(405,407) = 164835

LCM of 405 and 407

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

LCM of:
and

Least Common Multiple of 405 and 407

LCM of 405 and 407 is 164835

Least common multiple can be found by multiplying the highest exponent prime factors of 405 and 407. First we will calculate the prime factors of 405 and 407.

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 407


11 407
37 37
1

Prime factors of 407 are 11,37. Prime factorization of 407 in exponential form is:

407 = 111×371

Now multiplying the highest exponent prime factors to calculate the LCM of 405 and 407.

LCM(405,407) = 34×51×111×371
LCM(405,407) = 164835

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 407

List of positive integer factors of 407 that divides 407 without a remainder.

1, 11, 37, 407

Least Common Multiple of 405 and 407 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 407, than apply into the LCM equation.

GCF(405,407) = 1
LCM(405,407) = ( 405 × 407) / 1
LCM(405,407) = 164835 / 1
LCM(405,407) = 164835

Properties of LCM 405 and 407

(i) The LCM of 407 and 405 is associative

LCM of 405 and 407 = LCM of 407 and 405

Related Least Common Multiples of 405

Related Least Common Multiples of 407

Frequently Asked Questions on LCM of 405 and 407

1. What is the LCM of 405 and 407?

Answer: LCM of 405 and 407 is 164835.

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 407?

Answer: Factors of 407 are 1, 11, 37, 407. There are 4 integers that are factors of 407. The greatest factor of 407 is 407.

4. How to Find the LCM of 405 and 407?

Answer:

Least Common Multiple of 405 and 407 = 164835

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 407

407 = 11 x 37

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

LCM = 164835 = 3 x 3 x 3 x 3 x 5 x 11 x 37

Step 4: Therefore, the least common multiple of 405 and 407 is 164835.