Least Common Multiple of 34194 and 34200

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 34194 and 34200 the smallest integer that is 194905800 that is divisible by both numbers.

Least Common Multiple (LCM) of 34194 and 34200 is 194905800.

LCM(34194,34200) = 194905800

LCM of 34194 and 34200

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

LCM of:
and

Least Common Multiple of 34194 and 34200

LCM of 34194 and 34200 is 194905800

Least common multiple can be found by multiplying the highest exponent prime factors of 34194 and 34200. First we will calculate the prime factors of 34194 and 34200.

Prime Factorization of 34194


2 34194
3 17097
41 5699
139 139
1

Prime factors of 34194 are 2, 3, 41,139. Prime factorization of 34194 in exponential form is:

34194 = 21×31×411×1391

Prime Factorization of 34200


2 34200
2 17100
2 8550
3 4275
3 1425
5 475
5 95
19 19
1

Prime factors of 34200 are 2, 3, 5,19. Prime factorization of 34200 in exponential form is:

34200 = 23×32×52×191

Now multiplying the highest exponent prime factors to calculate the LCM of 34194 and 34200.

LCM(34194,34200) = 23×32×52×191×411×1391
LCM(34194,34200) = 194905800

Factors of 34194

List of positive integer factors of 34194 that divides 34194 without a remainder.

1, 2, 3, 6, 41, 82, 123, 139, 246, 278, 417, 834, 5699, 11398, 17097, 34194

Factors of 34200

List of positive integer factors of 34200 that divides 34200 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 19, 20, 24, 25, 30, 36, 38, 40, 45, 50, 57, 60, 72, 75, 76, 90, 95, 100, 114, 120, 150, 152, 171, 180, 190, 200, 225, 228, 285, 300, 342, 360, 380, 450, 456, 475, 570, 600, 684, 760, 855, 900, 950, 1140, 1368, 1425, 1710, 1800, 1900, 2280, 2850, 3420, 3800, 4275, 5700, 6840, 8550, 11400, 17100, 34200

Least Common Multiple of 34194 and 34200 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 34194 and 34200, than apply into the LCM equation.

GCF(34194,34200) = 6
LCM(34194,34200) = ( 34194 × 34200) / 6
LCM(34194,34200) = 1169434800 / 6
LCM(34194,34200) = 194905800

Properties of LCM 34194 and 34200

(i) The LCM of 34200 and 34194 is associative

LCM of 34194 and 34200 = LCM of 34200 and 34194

Related Least Common Multiples of 34194

Related Least Common Multiples of 34200

Frequently Asked Questions on LCM of 34194 and 34200

1. What is the LCM of 34194 and 34200?

Answer: LCM of 34194 and 34200 is 194905800.

2. What are the Factors of 34194?

Answer: Factors of 34194 are 1, 2, 3, 6, 41, 82, 123, 139, 246, 278, 417, 834, 5699, 11398, 17097, 34194. There are 16 integers that are factors of 34194. The greatest factor of 34194 is 34194.

3. What are the Factors of 34200?

Answer: Factors of 34200 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 19, 20, 24, 25, 30, 36, 38, 40, 45, 50, 57, 60, 72, 75, 76, 90, 95, 100, 114, 120, 150, 152, 171, 180, 190, 200, 225, 228, 285, 300, 342, 360, 380, 450, 456, 475, 570, 600, 684, 760, 855, 900, 950, 1140, 1368, 1425, 1710, 1800, 1900, 2280, 2850, 3420, 3800, 4275, 5700, 6840, 8550, 11400, 17100, 34200. There are 72 integers that are factors of 34200. The greatest factor of 34200 is 34200.

4. How to Find the LCM of 34194 and 34200?

Answer:

Least Common Multiple of 34194 and 34200 = 194905800

Step 1: Find the prime factorization of 34194

34194 = 2 x 3 x 41 x 139

Step 2: Find the prime factorization of 34200

34200 = 2 x 2 x 2 x 3 x 3 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 = 194905800 = 2 x 2 x 2 x 3 x 3 x 5 x 5 x 19 x 41 x 139

Step 4: Therefore, the least common multiple of 34194 and 34200 is 194905800.