Least Common Multiple of 189 and 195

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 189 and 195 the smallest integer that is 12285 that is divisible by both numbers.

Least Common Multiple (LCM) of 189 and 195 is 12285.

LCM(189,195) = 12285

LCM of 189 and 195

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

LCM of:
and

Least Common Multiple of 189 and 195

LCM of 189 and 195 is 12285

Least common multiple can be found by multiplying the highest exponent prime factors of 189 and 195. First we will calculate the prime factors of 189 and 195.

Prime Factorization of 189


3 189
3 63
3 21
7 7
1

Prime factors of 189 are 3,7. Prime factorization of 189 in exponential form is:

189 = 33×71

Prime Factorization of 195


3 195
5 65
13 13
1

Prime factors of 195 are 3, 5,13. Prime factorization of 195 in exponential form is:

195 = 31×51×131

Now multiplying the highest exponent prime factors to calculate the LCM of 189 and 195.

LCM(189,195) = 33×51×71×131
LCM(189,195) = 12285

Factors of 189

List of positive integer factors of 189 that divides 189 without a remainder.

1, 3, 7, 9, 21, 27, 63, 189

Factors of 195

List of positive integer factors of 195 that divides 195 without a remainder.

1, 3, 5, 13, 15, 39, 65, 195

Least Common Multiple of 189 and 195 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 189 and 195, than apply into the LCM equation.

GCF(189,195) = 3
LCM(189,195) = ( 189 × 195) / 3
LCM(189,195) = 36855 / 3
LCM(189,195) = 12285

Properties of LCM 189 and 195

(i) The LCM of 195 and 189 is associative

LCM of 189 and 195 = LCM of 195 and 189

Related Least Common Multiples of 189

Related Least Common Multiples of 195

Frequently Asked Questions on LCM of 189 and 195

1. What is the LCM of 189 and 195?

Answer: LCM of 189 and 195 is 12285.

2. What are the Factors of 189?

Answer: Factors of 189 are 1, 3, 7, 9, 21, 27, 63, 189. There are 8 integers that are factors of 189. The greatest factor of 189 is 189.

3. What are the Factors of 195?

Answer: Factors of 195 are 1, 3, 5, 13, 15, 39, 65, 195. There are 8 integers that are factors of 195. The greatest factor of 195 is 195.

4. How to Find the LCM of 189 and 195?

Answer:

Least Common Multiple of 189 and 195 = 12285

Step 1: Find the prime factorization of 189

189 = 3 x 3 x 3 x 7

Step 2: Find the prime factorization of 195

195 = 3 x 5 x 13

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

LCM = 12285 = 3 x 3 x 3 x 5 x 7 x 13

Step 4: Therefore, the least common multiple of 189 and 195 is 12285.