Least Common Multiple of 3405 and 3408

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 3405 and 3408 the smallest integer that is 3868080 that is divisible by both numbers.

Least Common Multiple (LCM) of 3405 and 3408 is 3868080.

LCM(3405,3408) = 3868080

LCM of 3405 and 3408

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

LCM of:
and

Least Common Multiple of 3405 and 3408

LCM of 3405 and 3408 is 3868080

Least common multiple can be found by multiplying the highest exponent prime factors of 3405 and 3408. First we will calculate the prime factors of 3405 and 3408.

Prime Factorization of 3405


3 3405
5 1135
227 227
1

Prime factors of 3405 are 3, 5,227. Prime factorization of 3405 in exponential form is:

3405 = 31×51×2271

Prime Factorization of 3408


2 3408
2 1704
2 852
2 426
3 213
71 71
1

Prime factors of 3408 are 2, 3,71. Prime factorization of 3408 in exponential form is:

3408 = 24×31×711

Now multiplying the highest exponent prime factors to calculate the LCM of 3405 and 3408.

LCM(3405,3408) = 24×31×51×711×2271
LCM(3405,3408) = 3868080

Factors of 3405

List of positive integer factors of 3405 that divides 3405 without a remainder.

1, 3, 5, 15, 227, 681, 1135, 3405

Factors of 3408

List of positive integer factors of 3408 that divides 3408 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 71, 142, 213, 284, 426, 568, 852, 1136, 1704, 3408

Least Common Multiple of 3405 and 3408 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3405 and 3408, than apply into the LCM equation.

GCF(3405,3408) = 3
LCM(3405,3408) = ( 3405 × 3408) / 3
LCM(3405,3408) = 11604240 / 3
LCM(3405,3408) = 3868080

Properties of LCM 3405 and 3408

(i) The LCM of 3408 and 3405 is associative

LCM of 3405 and 3408 = LCM of 3408 and 3405

Related Least Common Multiples of 3405

Related Least Common Multiples of 3408

Frequently Asked Questions on LCM of 3405 and 3408

1. What is the LCM of 3405 and 3408?

Answer: LCM of 3405 and 3408 is 3868080.

2. What are the Factors of 3405?

Answer: Factors of 3405 are 1, 3, 5, 15, 227, 681, 1135, 3405. There are 8 integers that are factors of 3405. The greatest factor of 3405 is 3405.

3. What are the Factors of 3408?

Answer: Factors of 3408 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 71, 142, 213, 284, 426, 568, 852, 1136, 1704, 3408. There are 20 integers that are factors of 3408. The greatest factor of 3408 is 3408.

4. How to Find the LCM of 3405 and 3408?

Answer:

Least Common Multiple of 3405 and 3408 = 3868080

Step 1: Find the prime factorization of 3405

3405 = 3 x 5 x 227

Step 2: Find the prime factorization of 3408

3408 = 2 x 2 x 2 x 2 x 3 x 71

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

LCM = 3868080 = 2 x 2 x 2 x 2 x 3 x 5 x 71 x 227

Step 4: Therefore, the least common multiple of 3405 and 3408 is 3868080.