Least Common Multiple of 10208 and 10212

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 10212 the smallest integer that is 26061024 that is divisible by both numbers.

Least Common Multiple (LCM) of 10208 and 10212 is 26061024.

LCM(10208,10212) = 26061024

LCM of 10208 and 10212

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

LCM of:
and

Least Common Multiple of 10208 and 10212

LCM of 10208 and 10212 is 26061024

Least common multiple can be found by multiplying the highest exponent prime factors of 10208 and 10212. First we will calculate the prime factors of 10208 and 10212.

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 10212


2 10212
2 5106
3 2553
23 851
37 37
1

Prime factors of 10212 are 2, 3, 23,37. Prime factorization of 10212 in exponential form is:

10212 = 22×31×231×371

Now multiplying the highest exponent prime factors to calculate the LCM of 10208 and 10212.

LCM(10208,10212) = 25×31×111×231×291×371
LCM(10208,10212) = 26061024

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 10212

List of positive integer factors of 10212 that divides 10212 without a remainder.

1, 2, 3, 4, 6, 12, 23, 37, 46, 69, 74, 92, 111, 138, 148, 222, 276, 444, 851, 1702, 2553, 3404, 5106, 10212

Least Common Multiple of 10208 and 10212 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 10212, than apply into the LCM equation.

GCF(10208,10212) = 4
LCM(10208,10212) = ( 10208 × 10212) / 4
LCM(10208,10212) = 104244096 / 4
LCM(10208,10212) = 26061024

Properties of LCM 10208 and 10212

(i) The LCM of 10212 and 10208 is associative

LCM of 10208 and 10212 = LCM of 10212 and 10208

Related Least Common Multiples of 10208

Related Least Common Multiples of 10212

Frequently Asked Questions on LCM of 10208 and 10212

1. What is the LCM of 10208 and 10212?

Answer: LCM of 10208 and 10212 is 26061024.

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 10212?

Answer: Factors of 10212 are 1, 2, 3, 4, 6, 12, 23, 37, 46, 69, 74, 92, 111, 138, 148, 222, 276, 444, 851, 1702, 2553, 3404, 5106, 10212. There are 24 integers that are factors of 10212. The greatest factor of 10212 is 10212.

4. How to Find the LCM of 10208 and 10212?

Answer:

Least Common Multiple of 10208 and 10212 = 26061024

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 10212

10212 = 2 x 2 x 3 x 23 x 37

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

LCM = 26061024 = 2 x 2 x 2 x 2 x 2 x 3 x 11 x 23 x 29 x 37

Step 4: Therefore, the least common multiple of 10208 and 10212 is 26061024.