Least Common Multiple of 189 and 192

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 192 the smallest integer that is 12096 that is divisible by both numbers.

Least Common Multiple (LCM) of 189 and 192 is 12096.

LCM(189,192) = 12096

LCM of 189 and 192

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

LCM of:
and

Least Common Multiple of 189 and 192

LCM of 189 and 192 is 12096

Least common multiple can be found by multiplying the highest exponent prime factors of 189 and 192. First we will calculate the prime factors of 189 and 192.

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 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

Now multiplying the highest exponent prime factors to calculate the LCM of 189 and 192.

LCM(189,192) = 26×33×71
LCM(189,192) = 12096

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 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

Least Common Multiple of 189 and 192 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 192, than apply into the LCM equation.

GCF(189,192) = 3
LCM(189,192) = ( 189 × 192) / 3
LCM(189,192) = 36288 / 3
LCM(189,192) = 12096

Properties of LCM 189 and 192

(i) The LCM of 192 and 189 is associative

LCM of 189 and 192 = LCM of 192 and 189

Related Least Common Multiples of 189

Related Least Common Multiples of 192

Frequently Asked Questions on LCM of 189 and 192

1. What is the LCM of 189 and 192?

Answer: LCM of 189 and 192 is 12096.

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 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.

4. How to Find the LCM of 189 and 192?

Answer:

Least Common Multiple of 189 and 192 = 12096

Step 1: Find the prime factorization of 189

189 = 3 x 3 x 3 x 7

Step 2: Find the prime factorization of 192

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

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

LCM = 12096 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 7

Step 4: Therefore, the least common multiple of 189 and 192 is 12096.