Least Common Multiple of 199 and 205

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 199 and 205 the smallest integer that is 40795 that is divisible by both numbers.

Least Common Multiple (LCM) of 199 and 205 is 40795.

LCM(199,205) = 40795

LCM of 199 and 205

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

LCM of:
and

Least Common Multiple of 199 and 205

LCM of 199 and 205 is 40795

Least common multiple can be found by multiplying the highest exponent prime factors of 199 and 205. First we will calculate the prime factors of 199 and 205.

Prime Factorization of 199


199 199
1

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

199 = 1991

Prime Factorization of 205


5 205
41 41
1

Prime factors of 205 are 5,41. Prime factorization of 205 in exponential form is:

205 = 51×411

Now multiplying the highest exponent prime factors to calculate the LCM of 199 and 205.

LCM(199,205) = 51×411×1991
LCM(199,205) = 40795

Factors of 199

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

1, 199

Factors of 205

List of positive integer factors of 205 that divides 205 without a remainder.

1, 5, 41, 205

Least Common Multiple of 199 and 205 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 199 and 205, than apply into the LCM equation.

GCF(199,205) = 1
LCM(199,205) = ( 199 × 205) / 1
LCM(199,205) = 40795 / 1
LCM(199,205) = 40795

Properties of LCM 199 and 205

(i) The LCM of 205 and 199 is associative

LCM of 199 and 205 = LCM of 205 and 199

Related Least Common Multiples of 199

Related Least Common Multiples of 205

Frequently Asked Questions on LCM of 199 and 205

1. What is the LCM of 199 and 205?

Answer: LCM of 199 and 205 is 40795.

2. 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.

3. What are the Factors of 205?

Answer: Factors of 205 are 1, 5, 41, 205. There are 4 integers that are factors of 205. The greatest factor of 205 is 205.

4. How to Find the LCM of 199 and 205?

Answer:

Least Common Multiple of 199 and 205 = 40795

Step 1: Find the prime factorization of 199

199 = 199

Step 2: Find the prime factorization of 205

205 = 5 x 41

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

LCM = 40795 = 5 x 41 x 199

Step 4: Therefore, the least common multiple of 199 and 205 is 40795.