Least Common Multiple of 208 and 209

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 208 and 209 the smallest integer that is 43472 that is divisible by both numbers.

Least Common Multiple (LCM) of 208 and 209 is 43472.

LCM(208,209) = 43472

LCM of 208 and 209

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

LCM of:
and

Least Common Multiple of 208 and 209

LCM of 208 and 209 is 43472

Least common multiple can be found by multiplying the highest exponent prime factors of 208 and 209. First we will calculate the prime factors of 208 and 209.

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

Prime Factorization of 209


11 209
19 19
1

Prime factors of 209 are 11,19. Prime factorization of 209 in exponential form is:

209 = 111×191

Now multiplying the highest exponent prime factors to calculate the LCM of 208 and 209.

LCM(208,209) = 24×111×131×191
LCM(208,209) = 43472

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

Factors of 209

List of positive integer factors of 209 that divides 209 without a remainder.

1, 11, 19, 209

Least Common Multiple of 208 and 209 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 208 and 209, than apply into the LCM equation.

GCF(208,209) = 1
LCM(208,209) = ( 208 × 209) / 1
LCM(208,209) = 43472 / 1
LCM(208,209) = 43472

Properties of LCM 208 and 209

(i) The LCM of 209 and 208 is associative

LCM of 208 and 209 = LCM of 209 and 208

Related Least Common Multiples of 208

Related Least Common Multiples of 209

Frequently Asked Questions on LCM of 208 and 209

1. What is the LCM of 208 and 209?

Answer: LCM of 208 and 209 is 43472.

2. 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.

3. What are the Factors of 209?

Answer: Factors of 209 are 1, 11, 19, 209. There are 4 integers that are factors of 209. The greatest factor of 209 is 209.

4. How to Find the LCM of 208 and 209?

Answer:

Least Common Multiple of 208 and 209 = 43472

Step 1: Find the prime factorization of 208

208 = 2 x 2 x 2 x 2 x 13

Step 2: Find the prime factorization of 209

209 = 11 x 19

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

LCM = 43472 = 2 x 2 x 2 x 2 x 11 x 13 x 19

Step 4: Therefore, the least common multiple of 208 and 209 is 43472.