Least Common Multiple of 3400 and 3405

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 3400 and 3405 the smallest integer that is 2315400 that is divisible by both numbers.

Least Common Multiple (LCM) of 3400 and 3405 is 2315400.

LCM(3400,3405) = 2315400

LCM of 3400 and 3405

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

LCM of:
and

Least Common Multiple of 3400 and 3405

LCM of 3400 and 3405 is 2315400

Least common multiple can be found by multiplying the highest exponent prime factors of 3400 and 3405. First we will calculate the prime factors of 3400 and 3405.

Prime Factorization of 3400


2 3400
2 1700
2 850
5 425
5 85
17 17
1

Prime factors of 3400 are 2, 5,17. Prime factorization of 3400 in exponential form is:

3400 = 23×52×171

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

Now multiplying the highest exponent prime factors to calculate the LCM of 3400 and 3405.

LCM(3400,3405) = 23×31×52×171×2271
LCM(3400,3405) = 2315400

Factors of 3400

List of positive integer factors of 3400 that divides 3400 without a remainder.

1, 2, 4, 5, 8, 10, 17, 20, 25, 34, 40, 50, 68, 85, 100, 136, 170, 200, 340, 425, 680, 850, 1700, 3400

Factors of 3405

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

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

Least Common Multiple of 3400 and 3405 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3400 and 3405, than apply into the LCM equation.

GCF(3400,3405) = 5
LCM(3400,3405) = ( 3400 × 3405) / 5
LCM(3400,3405) = 11577000 / 5
LCM(3400,3405) = 2315400

Properties of LCM 3400 and 3405

(i) The LCM of 3405 and 3400 is associative

LCM of 3400 and 3405 = LCM of 3405 and 3400

Related Least Common Multiples of 3400

Related Least Common Multiples of 3405

Frequently Asked Questions on LCM of 3400 and 3405

1. What is the LCM of 3400 and 3405?

Answer: LCM of 3400 and 3405 is 2315400.

2. What are the Factors of 3400?

Answer: Factors of 3400 are 1, 2, 4, 5, 8, 10, 17, 20, 25, 34, 40, 50, 68, 85, 100, 136, 170, 200, 340, 425, 680, 850, 1700, 3400. There are 24 integers that are factors of 3400. The greatest factor of 3400 is 3400.

3. 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.

4. How to Find the LCM of 3400 and 3405?

Answer:

Least Common Multiple of 3400 and 3405 = 2315400

Step 1: Find the prime factorization of 3400

3400 = 2 x 2 x 2 x 5 x 5 x 17

Step 2: Find the prime factorization of 3405

3405 = 3 x 5 x 227

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

LCM = 2315400 = 2 x 2 x 2 x 3 x 5 x 5 x 17 x 227

Step 4: Therefore, the least common multiple of 3400 and 3405 is 2315400.