Least Common Multiple of 15194 and 15200

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 15194 and 15200 the smallest integer that is 115474400 that is divisible by both numbers.

Least Common Multiple (LCM) of 15194 and 15200 is 115474400.

LCM(15194,15200) = 115474400

LCM of 15194 and 15200

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

LCM of:
and

Least Common Multiple of 15194 and 15200

LCM of 15194 and 15200 is 115474400

Least common multiple can be found by multiplying the highest exponent prime factors of 15194 and 15200. First we will calculate the prime factors of 15194 and 15200.

Prime Factorization of 15194


2 15194
71 7597
107 107
1

Prime factors of 15194 are 2, 71,107. Prime factorization of 15194 in exponential form is:

15194 = 21×711×1071

Prime Factorization of 15200


2 15200
2 7600
2 3800
2 1900
2 950
5 475
5 95
19 19
1

Prime factors of 15200 are 2, 5,19. Prime factorization of 15200 in exponential form is:

15200 = 25×52×191

Now multiplying the highest exponent prime factors to calculate the LCM of 15194 and 15200.

LCM(15194,15200) = 25×52×191×711×1071
LCM(15194,15200) = 115474400

Factors of 15194

List of positive integer factors of 15194 that divides 15194 without a remainder.

1, 2, 71, 107, 142, 214, 7597, 15194

Factors of 15200

List of positive integer factors of 15200 that divides 15200 without a remainder.

1, 2, 4, 5, 8, 10, 16, 19, 20, 25, 32, 38, 40, 50, 76, 80, 95, 100, 152, 160, 190, 200, 304, 380, 400, 475, 608, 760, 800, 950, 1520, 1900, 3040, 3800, 7600, 15200

Least Common Multiple of 15194 and 15200 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 15194 and 15200, than apply into the LCM equation.

GCF(15194,15200) = 2
LCM(15194,15200) = ( 15194 × 15200) / 2
LCM(15194,15200) = 230948800 / 2
LCM(15194,15200) = 115474400

Properties of LCM 15194 and 15200

(i) The LCM of 15200 and 15194 is associative

LCM of 15194 and 15200 = LCM of 15200 and 15194

Related Least Common Multiples of 15194

Related Least Common Multiples of 15200

Frequently Asked Questions on LCM of 15194 and 15200

1. What is the LCM of 15194 and 15200?

Answer: LCM of 15194 and 15200 is 115474400.

2. What are the Factors of 15194?

Answer: Factors of 15194 are 1, 2, 71, 107, 142, 214, 7597, 15194. There are 8 integers that are factors of 15194. The greatest factor of 15194 is 15194.

3. What are the Factors of 15200?

Answer: Factors of 15200 are 1, 2, 4, 5, 8, 10, 16, 19, 20, 25, 32, 38, 40, 50, 76, 80, 95, 100, 152, 160, 190, 200, 304, 380, 400, 475, 608, 760, 800, 950, 1520, 1900, 3040, 3800, 7600, 15200. There are 36 integers that are factors of 15200. The greatest factor of 15200 is 15200.

4. How to Find the LCM of 15194 and 15200?

Answer:

Least Common Multiple of 15194 and 15200 = 115474400

Step 1: Find the prime factorization of 15194

15194 = 2 x 71 x 107

Step 2: Find the prime factorization of 15200

15200 = 2 x 2 x 2 x 2 x 2 x 5 x 5 x 19

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

LCM = 115474400 = 2 x 2 x 2 x 2 x 2 x 5 x 5 x 19 x 71 x 107

Step 4: Therefore, the least common multiple of 15194 and 15200 is 115474400.