Least Common Multiple of 20400 and 20407

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 20400 and 20407 the smallest integer that is 416302800 that is divisible by both numbers.

Least Common Multiple (LCM) of 20400 and 20407 is 416302800.

LCM(20400,20407) = 416302800

LCM of 20400 and 20407

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

LCM of:
and

Least Common Multiple of 20400 and 20407

LCM of 20400 and 20407 is 416302800

Least common multiple can be found by multiplying the highest exponent prime factors of 20400 and 20407. First we will calculate the prime factors of 20400 and 20407.

Prime Factorization of 20400


2 20400
2 10200
2 5100
2 2550
3 1275
5 425
5 85
17 17
1

Prime factors of 20400 are 2, 3, 5,17. Prime factorization of 20400 in exponential form is:

20400 = 24×31×52×171

Prime Factorization of 20407


20407 20407
1

Prime factors of 20407 are 20407. Prime factorization of 20407 in exponential form is:

20407 = 204071

Now multiplying the highest exponent prime factors to calculate the LCM of 20400 and 20407.

LCM(20400,20407) = 24×31×52×171×204071
LCM(20400,20407) = 416302800

Factors of 20400

List of positive integer factors of 20400 that divides 20400 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 24, 25, 30, 34, 40, 48, 50, 51, 60, 68, 75, 80, 85, 100, 102, 120, 136, 150, 170, 200, 204, 240, 255, 272, 300, 340, 400, 408, 425, 510, 600, 680, 816, 850, 1020, 1200, 1275, 1360, 1700, 2040, 2550, 3400, 4080, 5100, 6800, 10200, 20400

Factors of 20407

List of positive integer factors of 20407 that divides 20407 without a remainder.

1, 20407

Least Common Multiple of 20400 and 20407 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 20400 and 20407, than apply into the LCM equation.

GCF(20400,20407) = 1
LCM(20400,20407) = ( 20400 × 20407) / 1
LCM(20400,20407) = 416302800 / 1
LCM(20400,20407) = 416302800

Properties of LCM 20400 and 20407

(i) The LCM of 20407 and 20400 is associative

LCM of 20400 and 20407 = LCM of 20407 and 20400

Related Least Common Multiples of 20400

Related Least Common Multiples of 20407

Frequently Asked Questions on LCM of 20400 and 20407

1. What is the LCM of 20400 and 20407?

Answer: LCM of 20400 and 20407 is 416302800.

2. What are the Factors of 20400?

Answer: Factors of 20400 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 24, 25, 30, 34, 40, 48, 50, 51, 60, 68, 75, 80, 85, 100, 102, 120, 136, 150, 170, 200, 204, 240, 255, 272, 300, 340, 400, 408, 425, 510, 600, 680, 816, 850, 1020, 1200, 1275, 1360, 1700, 2040, 2550, 3400, 4080, 5100, 6800, 10200, 20400. There are 60 integers that are factors of 20400. The greatest factor of 20400 is 20400.

3. What are the Factors of 20407?

Answer: Factors of 20407 are 1, 20407. There are 2 integers that are factors of 20407. The greatest factor of 20407 is 20407.

4. How to Find the LCM of 20400 and 20407?

Answer:

Least Common Multiple of 20400 and 20407 = 416302800

Step 1: Find the prime factorization of 20400

20400 = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 17

Step 2: Find the prime factorization of 20407

20407 = 20407

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

LCM = 416302800 = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 17 x 20407

Step 4: Therefore, the least common multiple of 20400 and 20407 is 416302800.