Least Common Multiple of 208 and 215

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 215 the smallest integer that is 44720 that is divisible by both numbers.

Least Common Multiple (LCM) of 208 and 215 is 44720.

LCM(208,215) = 44720

LCM of 208 and 215

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

LCM of:
and

Least Common Multiple of 208 and 215

LCM of 208 and 215 is 44720

Least common multiple can be found by multiplying the highest exponent prime factors of 208 and 215. First we will calculate the prime factors of 208 and 215.

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 215


5 215
43 43
1

Prime factors of 215 are 5,43. Prime factorization of 215 in exponential form is:

215 = 51×431

Now multiplying the highest exponent prime factors to calculate the LCM of 208 and 215.

LCM(208,215) = 24×51×131×431
LCM(208,215) = 44720

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 215

List of positive integer factors of 215 that divides 215 without a remainder.

1, 5, 43, 215

Least Common Multiple of 208 and 215 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 215, than apply into the LCM equation.

GCF(208,215) = 1
LCM(208,215) = ( 208 × 215) / 1
LCM(208,215) = 44720 / 1
LCM(208,215) = 44720

Properties of LCM 208 and 215

(i) The LCM of 215 and 208 is associative

LCM of 208 and 215 = LCM of 215 and 208

Related Least Common Multiples of 208

Related Least Common Multiples of 215

Frequently Asked Questions on LCM of 208 and 215

1. What is the LCM of 208 and 215?

Answer: LCM of 208 and 215 is 44720.

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 215?

Answer: Factors of 215 are 1, 5, 43, 215. There are 4 integers that are factors of 215. The greatest factor of 215 is 215.

4. How to Find the LCM of 208 and 215?

Answer:

Least Common Multiple of 208 and 215 = 44720

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 215

215 = 5 x 43

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

LCM = 44720 = 2 x 2 x 2 x 2 x 5 x 13 x 43

Step 4: Therefore, the least common multiple of 208 and 215 is 44720.