Least Common Multiple of 10199 and 10205

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

• Least Common Multiple of 10199 and 10205 by Prime method
• Least Common Multiple of 10199 and 10205 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 10199 and 10205. First we will calculate the prime factors of 10199 and 10205.

Prime Factorization of 10199

Prime factors of 10199 are 7, 31,47. Prime factorization of 10199 in exponential form is:

10199 = 7¹×31¹×47¹

Prime Factorization of 10205

Prime factors of 10205 are 5, 13,157. Prime factorization of 10205 in exponential form is:

10205 = 5¹×13¹×157¹

Now multiplying the highest exponent prime factors to calculate the LCM of 10199 and 10205.

LCM(10199,10205) = 5¹×7¹×13¹×31¹×47¹×157¹
LCM(10199,10205) = 104080795

Factors of 10199

List of positive integer factors of 10199 that divides 10199 without a remainder.

1, 7, 31, 47, 217, 329, 1457, 10199

Factors of 10205

List of positive integer factors of 10205 that divides 10205 without a remainder.

1, 5, 13, 65, 157, 785, 2041, 10205

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10199 and 10205, than apply into the LCM equation.

GCF(10199,10205) = 1
LCM(10199,10205) = ( 10199 × 10205) / 1
LCM(10199,10205) = 104080795 / 1
LCM(10199,10205) = 104080795

(i) The LCM of 10205 and 10199 is associative

LCM of 10199 and 10205 = LCM of 10205 and 10199

1. What is the LCM of 10199 and 10205?

Answer: LCM of 10199 and 10205 is 104080795.

2. What are the Factors of 10199?

Answer: Factors of 10199 are 1, 7, 31, 47, 217, 329, 1457, 10199. There are 8 integers that are factors of 10199. The greatest factor of 10199 is 10199.

3. What are the Factors of 10205?

Answer: Factors of 10205 are 1, 5, 13, 65, 157, 785, 2041, 10205. There are 8 integers that are factors of 10205. The greatest factor of 10205 is 10205.

4. How to Find the LCM of 10199 and 10205?

Answer:

Least Common Multiple of 10199 and 10205 = 104080795

Step 1: Find the prime factorization of 10199

10199 = 7 x 31 x 47

Step 2: Find the prime factorization of 10205

10205 = 5 x 13 x 157

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

LCM = 104080795 = 5 x 7 x 13 x 31 x 47 x 157

Step 4: Therefore, the least common multiple of 10199 and 10205 is 104080795.