Least Common Multiple of 192 and 198

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 198 the smallest integer that is 6336 that is divisible by both numbers.

Least Common Multiple (LCM) of 192 and 198 is 6336.

LCM(192,198) = 6336

LCM of 192 and 198

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

LCM of:
and

Least Common Multiple of 192 and 198

LCM of 192 and 198 is 6336

Least common multiple can be found by multiplying the highest exponent prime factors of 192 and 198. First we will calculate the prime factors of 192 and 198.

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 198


2 198
3 99
3 33
11 11
1

Prime factors of 198 are 2, 3,11. Prime factorization of 198 in exponential form is:

198 = 21×32×111

Now multiplying the highest exponent prime factors to calculate the LCM of 192 and 198.

LCM(192,198) = 26×32×111
LCM(192,198) = 6336

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 198

List of positive integer factors of 198 that divides 198 without a remainder.

1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198

Least Common Multiple of 192 and 198 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 198, than apply into the LCM equation.

GCF(192,198) = 6
LCM(192,198) = ( 192 × 198) / 6
LCM(192,198) = 38016 / 6
LCM(192,198) = 6336

Properties of LCM 192 and 198

(i) The LCM of 198 and 192 is associative

LCM of 192 and 198 = LCM of 198 and 192

Related Least Common Multiples of 192

Related Least Common Multiples of 198

Frequently Asked Questions on LCM of 192 and 198

1. What is the LCM of 192 and 198?

Answer: LCM of 192 and 198 is 6336.

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 198?

Answer: Factors of 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198. There are 12 integers that are factors of 198. The greatest factor of 198 is 198.

4. How to Find the LCM of 192 and 198?

Answer:

Least Common Multiple of 192 and 198 = 6336

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 198

198 = 2 x 3 x 3 x 11

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

LCM = 6336 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 11

Step 4: Therefore, the least common multiple of 192 and 198 is 6336.