Least Common Multiple of 205 and 208

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 205 and 208 the smallest integer that is 42640 that is divisible by both numbers.

Least Common Multiple (LCM) of 205 and 208 is 42640.

LCM(205,208) = 42640

LCM of 205 and 208

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

LCM of:
and

Least Common Multiple of 205 and 208

LCM of 205 and 208 is 42640

Least common multiple can be found by multiplying the highest exponent prime factors of 205 and 208. First we will calculate the prime factors of 205 and 208.

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

Prime Factorization of 208


2 208
2 104
2 52
2 26
13 13
1

Prime factors of 208 are 2,13. Prime factorization of 208 in exponential form is:

208 = 24×131

Now multiplying the highest exponent prime factors to calculate the LCM of 205 and 208.

LCM(205,208) = 24×51×131×411
LCM(205,208) = 42640

Factors of 205

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

1, 5, 41, 205

Factors of 208

List of positive integer factors of 208 that divides 208 without a remainder.

1, 2, 4, 8, 13, 16, 26, 52, 104, 208

Least Common Multiple of 205 and 208 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 205 and 208, than apply into the LCM equation.

GCF(205,208) = 1
LCM(205,208) = ( 205 × 208) / 1
LCM(205,208) = 42640 / 1
LCM(205,208) = 42640

Properties of LCM 205 and 208

(i) The LCM of 208 and 205 is associative

LCM of 205 and 208 = LCM of 208 and 205

Related Least Common Multiples of 205

Related Least Common Multiples of 208

Frequently Asked Questions on LCM of 205 and 208

1. What is the LCM of 205 and 208?

Answer: LCM of 205 and 208 is 42640.

2. 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.

3. What are the Factors of 208?

Answer: Factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208. There are 10 integers that are factors of 208. The greatest factor of 208 is 208.

4. How to Find the LCM of 205 and 208?

Answer:

Least Common Multiple of 205 and 208 = 42640

Step 1: Find the prime factorization of 205

205 = 5 x 41

Step 2: Find the prime factorization of 208

208 = 2 x 2 x 2 x 2 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 = 42640 = 2 x 2 x 2 x 2 x 5 x 13 x 41

Step 4: Therefore, the least common multiple of 205 and 208 is 42640.