Least Common Multiple of 192 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 192 and 195 the smallest integer that is 12480 that is divisible by both numbers.

Least Common Multiple (LCM) of 192 and 195 is 12480.

LCM(192,195) = 12480

LCM of 192 and 195

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

LCM of:
and

Least Common Multiple of 192 and 195

LCM of 192 and 195 is 12480

Least common multiple can be found by multiplying the highest exponent prime factors of 192 and 195. First we will calculate the prime factors of 192 and 195.

Prime Factorization of 192


2 192
2 96
2 48
2 24
2 12
2 6
3 3
1

Prime factors of 192 are 2,3. Prime factorization of 192 in exponential form is:

192 = 26×31

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 192 and 195.

LCM(192,195) = 26×31×51×131
LCM(192,195) = 12480

Factors of 192

List of positive integer factors of 192 that divides 192 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192

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 192 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 192 and 195, than apply into the LCM equation.

GCF(192,195) = 3
LCM(192,195) = ( 192 × 195) / 3
LCM(192,195) = 37440 / 3
LCM(192,195) = 12480

Properties of LCM 192 and 195

(i) The LCM of 195 and 192 is associative

LCM of 192 and 195 = LCM of 195 and 192

Related Least Common Multiples of 192

Related Least Common Multiples of 195

Frequently Asked Questions on LCM of 192 and 195

1. What is the LCM of 192 and 195?

Answer: LCM of 192 and 195 is 12480.

2. What are the Factors of 192?

Answer: Factors of 192 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192. There are 14 integers that are factors of 192. The greatest factor of 192 is 192.

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 192 and 195?

Answer:

Least Common Multiple of 192 and 195 = 12480

Step 1: Find the prime factorization of 192

192 = 2 x 2 x 2 x 2 x 2 x 2 x 3

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 = 12480 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 13

Step 4: Therefore, the least common multiple of 192 and 195 is 12480.