Least Common Multiple of 10208 and 10215

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 10208 and 10215 the smallest integer that is 104274720 that is divisible by both numbers.

Least Common Multiple (LCM) of 10208 and 10215 is 104274720.

LCM(10208,10215) = 104274720

LCM of 10208 and 10215

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

LCM of:
and

Least Common Multiple of 10208 and 10215

LCM of 10208 and 10215 is 104274720

Least common multiple can be found by multiplying the highest exponent prime factors of 10208 and 10215. First we will calculate the prime factors of 10208 and 10215.

Prime Factorization of 10208


2 10208
2 5104
2 2552
2 1276
2 638
11 319
29 29
1

Prime factors of 10208 are 2, 11,29. Prime factorization of 10208 in exponential form is:

10208 = 25×111×291

Prime Factorization of 10215


3 10215
3 3405
5 1135
227 227
1

Prime factors of 10215 are 3, 5,227. Prime factorization of 10215 in exponential form is:

10215 = 32×51×2271

Now multiplying the highest exponent prime factors to calculate the LCM of 10208 and 10215.

LCM(10208,10215) = 25×32×51×111×291×2271
LCM(10208,10215) = 104274720

Factors of 10208

List of positive integer factors of 10208 that divides 10208 without a remainder.

1, 2, 4, 8, 11, 16, 22, 29, 32, 44, 58, 88, 116, 176, 232, 319, 352, 464, 638, 928, 1276, 2552, 5104, 10208

Factors of 10215

List of positive integer factors of 10215 that divides 10215 without a remainder.

1, 3, 5, 9, 15, 45, 227, 681, 1135, 2043, 3405, 10215

Least Common Multiple of 10208 and 10215 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10208 and 10215, than apply into the LCM equation.

GCF(10208,10215) = 1
LCM(10208,10215) = ( 10208 × 10215) / 1
LCM(10208,10215) = 104274720 / 1
LCM(10208,10215) = 104274720

Properties of LCM 10208 and 10215

(i) The LCM of 10215 and 10208 is associative

LCM of 10208 and 10215 = LCM of 10215 and 10208

Related Least Common Multiples of 10208

Related Least Common Multiples of 10215

Frequently Asked Questions on LCM of 10208 and 10215

1. What is the LCM of 10208 and 10215?

Answer: LCM of 10208 and 10215 is 104274720.

2. What are the Factors of 10208?

Answer: Factors of 10208 are 1, 2, 4, 8, 11, 16, 22, 29, 32, 44, 58, 88, 116, 176, 232, 319, 352, 464, 638, 928, 1276, 2552, 5104, 10208. There are 24 integers that are factors of 10208. The greatest factor of 10208 is 10208.

3. What are the Factors of 10215?

Answer: Factors of 10215 are 1, 3, 5, 9, 15, 45, 227, 681, 1135, 2043, 3405, 10215. There are 12 integers that are factors of 10215. The greatest factor of 10215 is 10215.

4. How to Find the LCM of 10208 and 10215?

Answer:

Least Common Multiple of 10208 and 10215 = 104274720

Step 1: Find the prime factorization of 10208

10208 = 2 x 2 x 2 x 2 x 2 x 11 x 29

Step 2: Find the prime factorization of 10215

10215 = 3 x 3 x 5 x 227

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

LCM = 104274720 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 11 x 29 x 227

Step 4: Therefore, the least common multiple of 10208 and 10215 is 104274720.