Least Common Multiple of 20400 and 20404

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 20404 the smallest integer that is 104060400 that is divisible by both numbers.

Least Common Multiple (LCM) of 20400 and 20404 is 104060400.

LCM(20400,20404) = 104060400

LCM of 20400 and 20404

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

LCM of:
and

Least Common Multiple of 20400 and 20404

LCM of 20400 and 20404 is 104060400

Least common multiple can be found by multiplying the highest exponent prime factors of 20400 and 20404. First we will calculate the prime factors of 20400 and 20404.

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 20404


2 20404
2 10202
5101 5101
1

Prime factors of 20404 are 2,5101. Prime factorization of 20404 in exponential form is:

20404 = 22×51011

Now multiplying the highest exponent prime factors to calculate the LCM of 20400 and 20404.

LCM(20400,20404) = 24×31×52×171×51011
LCM(20400,20404) = 104060400

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 20404

List of positive integer factors of 20404 that divides 20404 without a remainder.

1, 2, 4, 5101, 10202, 20404

Least Common Multiple of 20400 and 20404 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 20404, than apply into the LCM equation.

GCF(20400,20404) = 4
LCM(20400,20404) = ( 20400 × 20404) / 4
LCM(20400,20404) = 416241600 / 4
LCM(20400,20404) = 104060400

Properties of LCM 20400 and 20404

(i) The LCM of 20404 and 20400 is associative

LCM of 20400 and 20404 = LCM of 20404 and 20400

Related Least Common Multiples of 20400

Related Least Common Multiples of 20404

Frequently Asked Questions on LCM of 20400 and 20404

1. What is the LCM of 20400 and 20404?

Answer: LCM of 20400 and 20404 is 104060400.

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 20404?

Answer: Factors of 20404 are 1, 2, 4, 5101, 10202, 20404. There are 6 integers that are factors of 20404. The greatest factor of 20404 is 20404.

4. How to Find the LCM of 20400 and 20404?

Answer:

Least Common Multiple of 20400 and 20404 = 104060400

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 20404

20404 = 2 x 2 x 5101

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

LCM = 104060400 = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 17 x 5101

Step 4: Therefore, the least common multiple of 20400 and 20404 is 104060400.