Least Common Multiple of 206 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 206 and 208 the smallest integer that is 21424 that is divisible by both numbers.

Least Common Multiple (LCM) of 206 and 208 is 21424.

LCM(206,208) = 21424

LCM of 206 and 208

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

LCM of:
and

Least Common Multiple of 206 and 208

LCM of 206 and 208 is 21424

Least common multiple can be found by multiplying the highest exponent prime factors of 206 and 208. First we will calculate the prime factors of 206 and 208.

Prime Factorization of 206


2 206
103 103
1

Prime factors of 206 are 2,103. Prime factorization of 206 in exponential form is:

206 = 21×1031

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 206 and 208.

LCM(206,208) = 24×131×1031
LCM(206,208) = 21424

Factors of 206

List of positive integer factors of 206 that divides 206 without a remainder.

1, 2, 103, 206

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 206 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 206 and 208, than apply into the LCM equation.

GCF(206,208) = 2
LCM(206,208) = ( 206 × 208) / 2
LCM(206,208) = 42848 / 2
LCM(206,208) = 21424

Properties of LCM 206 and 208

(i) The LCM of 208 and 206 is associative

LCM of 206 and 208 = LCM of 208 and 206

Related Least Common Multiples of 206

Related Least Common Multiples of 208

Frequently Asked Questions on LCM of 206 and 208

1. What is the LCM of 206 and 208?

Answer: LCM of 206 and 208 is 21424.

2. What are the Factors of 206?

Answer: Factors of 206 are 1, 2, 103, 206. There are 4 integers that are factors of 206. The greatest factor of 206 is 206.

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 206 and 208?

Answer:

Least Common Multiple of 206 and 208 = 21424

Step 1: Find the prime factorization of 206

206 = 2 x 103

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 = 21424 = 2 x 2 x 2 x 2 x 13 x 103

Step 4: Therefore, the least common multiple of 206 and 208 is 21424.