Least Common Multiple of 208 and 213

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 213 the smallest integer that is 44304 that is divisible by both numbers.

Least Common Multiple (LCM) of 208 and 213 is 44304.

LCM(208,213) = 44304

LCM of 208 and 213

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

LCM of:
and

Least Common Multiple of 208 and 213

LCM of 208 and 213 is 44304

Least common multiple can be found by multiplying the highest exponent prime factors of 208 and 213. First we will calculate the prime factors of 208 and 213.

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 213


3 213
71 71
1

Prime factors of 213 are 3,71. Prime factorization of 213 in exponential form is:

213 = 31×711

Now multiplying the highest exponent prime factors to calculate the LCM of 208 and 213.

LCM(208,213) = 24×31×131×711
LCM(208,213) = 44304

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 213

List of positive integer factors of 213 that divides 213 without a remainder.

1, 3, 71, 213

Least Common Multiple of 208 and 213 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 213, than apply into the LCM equation.

GCF(208,213) = 1
LCM(208,213) = ( 208 × 213) / 1
LCM(208,213) = 44304 / 1
LCM(208,213) = 44304

Properties of LCM 208 and 213

(i) The LCM of 213 and 208 is associative

LCM of 208 and 213 = LCM of 213 and 208

Related Least Common Multiples of 208

Related Least Common Multiples of 213

Frequently Asked Questions on LCM of 208 and 213

1. What is the LCM of 208 and 213?

Answer: LCM of 208 and 213 is 44304.

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 213?

Answer: Factors of 213 are 1, 3, 71, 213. There are 4 integers that are factors of 213. The greatest factor of 213 is 213.

4. How to Find the LCM of 208 and 213?

Answer:

Least Common Multiple of 208 and 213 = 44304

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 213

213 = 3 x 71

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

LCM = 44304 = 2 x 2 x 2 x 2 x 3 x 13 x 71

Step 4: Therefore, the least common multiple of 208 and 213 is 44304.