Least Common Multiple of 10165 and 10166

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

• Least Common Multiple of 10165 and 10166 by Prime method
• Least Common Multiple of 10165 and 10166 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 10165 and 10166. First we will calculate the prime factors of 10165 and 10166.

Prime Factorization of 10165

Prime factors of 10165 are 5, 19,107. Prime factorization of 10165 in exponential form is:

10165 = 5¹×19¹×107¹

Prime Factorization of 10166

Prime factors of 10166 are 2, 13, 17,23. Prime factorization of 10166 in exponential form is:

10166 = 2¹×13¹×17¹×23¹

Now multiplying the highest exponent prime factors to calculate the LCM of 10165 and 10166.

LCM(10165,10166) = 2¹×5¹×13¹×17¹×19¹×23¹×107¹
LCM(10165,10166) = 103337390

Factors of 10165

List of positive integer factors of 10165 that divides 10165 without a remainder.

1, 5, 19, 95, 107, 535, 2033, 10165

Factors of 10166

List of positive integer factors of 10166 that divides 10166 without a remainder.

1, 2, 13, 17, 23, 26, 34, 46, 221, 299, 391, 442, 598, 782, 5083, 10166

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10165 and 10166, than apply into the LCM equation.

GCF(10165,10166) = 1
LCM(10165,10166) = ( 10165 × 10166) / 1
LCM(10165,10166) = 103337390 / 1
LCM(10165,10166) = 103337390

(i) The LCM of 10166 and 10165 is associative

LCM of 10165 and 10166 = LCM of 10166 and 10165

1. What is the LCM of 10165 and 10166?

Answer: LCM of 10165 and 10166 is 103337390.

2. What are the Factors of 10165?

Answer: Factors of 10165 are 1, 5, 19, 95, 107, 535, 2033, 10165. There are 8 integers that are factors of 10165. The greatest factor of 10165 is 10165.

3. What are the Factors of 10166?

Answer: Factors of 10166 are 1, 2, 13, 17, 23, 26, 34, 46, 221, 299, 391, 442, 598, 782, 5083, 10166. There are 16 integers that are factors of 10166. The greatest factor of 10166 is 10166.

4. How to Find the LCM of 10165 and 10166?

Answer:

Least Common Multiple of 10165 and 10166 = 103337390

Step 1: Find the prime factorization of 10165

10165 = 5 x 19 x 107

Step 2: Find the prime factorization of 10166

10166 = 2 x 13 x 17 x 23

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

LCM = 103337390 = 2 x 5 x 13 x 17 x 19 x 23 x 107

Step 4: Therefore, the least common multiple of 10165 and 10166 is 103337390.