Least Common Multiple of 192 and 199

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 199 the smallest integer that is 38208 that is divisible by both numbers.

Least Common Multiple (LCM) of 192 and 199 is 38208.

LCM(192,199) = 38208

LCM of 192 and 199

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

LCM of:
and

Least Common Multiple of 192 and 199

LCM of 192 and 199 is 38208

Least common multiple can be found by multiplying the highest exponent prime factors of 192 and 199. First we will calculate the prime factors of 192 and 199.

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 199


199 199
1

Prime factors of 199 are 199. Prime factorization of 199 in exponential form is:

199 = 1991

Now multiplying the highest exponent prime factors to calculate the LCM of 192 and 199.

LCM(192,199) = 26×31×1991
LCM(192,199) = 38208

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 199

List of positive integer factors of 199 that divides 199 without a remainder.

1, 199

Least Common Multiple of 192 and 199 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 199, than apply into the LCM equation.

GCF(192,199) = 1
LCM(192,199) = ( 192 × 199) / 1
LCM(192,199) = 38208 / 1
LCM(192,199) = 38208

Properties of LCM 192 and 199

(i) The LCM of 199 and 192 is associative

LCM of 192 and 199 = LCM of 199 and 192

Related Least Common Multiples of 192

Related Least Common Multiples of 199

Frequently Asked Questions on LCM of 192 and 199

1. What is the LCM of 192 and 199?

Answer: LCM of 192 and 199 is 38208.

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 199?

Answer: Factors of 199 are 1, 199. There are 2 integers that are factors of 199. The greatest factor of 199 is 199.

4. How to Find the LCM of 192 and 199?

Answer:

Least Common Multiple of 192 and 199 = 38208

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 199

199 = 199

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

LCM = 38208 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 199

Step 4: Therefore, the least common multiple of 192 and 199 is 38208.