Least Common Multiple of 10400 and 10407

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 10400 and 10407 the smallest integer that is 108232800 that is divisible by both numbers.

Least Common Multiple (LCM) of 10400 and 10407 is 108232800.

LCM(10400,10407) = 108232800

LCM of 10400 and 10407

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

LCM of:
and

Least Common Multiple of 10400 and 10407

LCM of 10400 and 10407 is 108232800

Least common multiple can be found by multiplying the highest exponent prime factors of 10400 and 10407. First we will calculate the prime factors of 10400 and 10407.

Prime Factorization of 10400


2 10400
2 5200
2 2600
2 1300
2 650
5 325
5 65
13 13
1

Prime factors of 10400 are 2, 5,13. Prime factorization of 10400 in exponential form is:

10400 = 25×52×131

Prime Factorization of 10407


3 10407
3469 3469
1

Prime factors of 10407 are 3,3469. Prime factorization of 10407 in exponential form is:

10407 = 31×34691

Now multiplying the highest exponent prime factors to calculate the LCM of 10400 and 10407.

LCM(10400,10407) = 25×31×52×131×34691
LCM(10400,10407) = 108232800

Factors of 10400

List of positive integer factors of 10400 that divides 10400 without a remainder.

1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 32, 40, 50, 52, 65, 80, 100, 104, 130, 160, 200, 208, 260, 325, 400, 416, 520, 650, 800, 1040, 1300, 2080, 2600, 5200, 10400

Factors of 10407

List of positive integer factors of 10407 that divides 10407 without a remainder.

1, 3, 3469, 10407

Least Common Multiple of 10400 and 10407 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10400 and 10407, than apply into the LCM equation.

GCF(10400,10407) = 1
LCM(10400,10407) = ( 10400 × 10407) / 1
LCM(10400,10407) = 108232800 / 1
LCM(10400,10407) = 108232800

Properties of LCM 10400 and 10407

(i) The LCM of 10407 and 10400 is associative

LCM of 10400 and 10407 = LCM of 10407 and 10400

Related Least Common Multiples of 10400

Related Least Common Multiples of 10407

Frequently Asked Questions on LCM of 10400 and 10407

1. What is the LCM of 10400 and 10407?

Answer: LCM of 10400 and 10407 is 108232800.

2. What are the Factors of 10400?

Answer: Factors of 10400 are 1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 32, 40, 50, 52, 65, 80, 100, 104, 130, 160, 200, 208, 260, 325, 400, 416, 520, 650, 800, 1040, 1300, 2080, 2600, 5200, 10400. There are 36 integers that are factors of 10400. The greatest factor of 10400 is 10400.

3. What are the Factors of 10407?

Answer: Factors of 10407 are 1, 3, 3469, 10407. There are 4 integers that are factors of 10407. The greatest factor of 10407 is 10407.

4. How to Find the LCM of 10400 and 10407?

Answer:

Least Common Multiple of 10400 and 10407 = 108232800

Step 1: Find the prime factorization of 10400

10400 = 2 x 2 x 2 x 2 x 2 x 5 x 5 x 13

Step 2: Find the prime factorization of 10407

10407 = 3 x 3469

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

LCM = 108232800 = 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5 x 13 x 3469

Step 4: Therefore, the least common multiple of 10400 and 10407 is 108232800.