Least Common Multiple of 20394 and 20400

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 20394 and 20400 the smallest integer that is 69339600 that is divisible by both numbers.

Least Common Multiple (LCM) of 20394 and 20400 is 69339600.

LCM(20394,20400) = 69339600

LCM of 20394 and 20400

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

LCM of:
and

Least Common Multiple of 20394 and 20400

LCM of 20394 and 20400 is 69339600

Least common multiple can be found by multiplying the highest exponent prime factors of 20394 and 20400. First we will calculate the prime factors of 20394 and 20400.

Prime Factorization of 20394


2 20394
3 10197
3 3399
11 1133
103 103
1

Prime factors of 20394 are 2, 3, 11,103. Prime factorization of 20394 in exponential form is:

20394 = 21×32×111×1031

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

Now multiplying the highest exponent prime factors to calculate the LCM of 20394 and 20400.

LCM(20394,20400) = 24×32×52×111×171×1031
LCM(20394,20400) = 69339600

Factors of 20394

List of positive integer factors of 20394 that divides 20394 without a remainder.

1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 103, 198, 206, 309, 618, 927, 1133, 1854, 2266, 3399, 6798, 10197, 20394

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

Least Common Multiple of 20394 and 20400 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 20394 and 20400, than apply into the LCM equation.

GCF(20394,20400) = 6
LCM(20394,20400) = ( 20394 × 20400) / 6
LCM(20394,20400) = 416037600 / 6
LCM(20394,20400) = 69339600

Properties of LCM 20394 and 20400

(i) The LCM of 20400 and 20394 is associative

LCM of 20394 and 20400 = LCM of 20400 and 20394

Related Least Common Multiples of 20394

Related Least Common Multiples of 20400

Frequently Asked Questions on LCM of 20394 and 20400

1. What is the LCM of 20394 and 20400?

Answer: LCM of 20394 and 20400 is 69339600.

2. What are the Factors of 20394?

Answer: Factors of 20394 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 103, 198, 206, 309, 618, 927, 1133, 1854, 2266, 3399, 6798, 10197, 20394. There are 24 integers that are factors of 20394. The greatest factor of 20394 is 20394.

3. 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.

4. How to Find the LCM of 20394 and 20400?

Answer:

Least Common Multiple of 20394 and 20400 = 69339600

Step 1: Find the prime factorization of 20394

20394 = 2 x 3 x 3 x 11 x 103

Step 2: Find the prime factorization of 20400

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

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

LCM = 69339600 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5 x 11 x 17 x 103

Step 4: Therefore, the least common multiple of 20394 and 20400 is 69339600.