Least Common Multiple of 10110 and 10117

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

• Least Common Multiple of 10110 and 10117 by Prime method
• Least Common Multiple of 10110 and 10117 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 10110 and 10117. First we will calculate the prime factors of 10110 and 10117.

Prime Factorization of 10110

Prime factors of 10110 are 2, 3, 5,337. Prime factorization of 10110 in exponential form is:

10110 = 2¹×3¹×5¹×337¹

Prime Factorization of 10117

Prime factors of 10117 are 67,151. Prime factorization of 10117 in exponential form is:

10117 = 67¹×151¹

Now multiplying the highest exponent prime factors to calculate the LCM of 10110 and 10117.

LCM(10110,10117) = 2¹×3¹×5¹×67¹×151¹×337¹
LCM(10110,10117) = 102282870

Factors of 10110

List of positive integer factors of 10110 that divides 10110 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 337, 674, 1011, 1685, 2022, 3370, 5055, 10110

Factors of 10117

List of positive integer factors of 10117 that divides 10117 without a remainder.

1, 67, 151, 10117

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10110 and 10117, than apply into the LCM equation.

GCF(10110,10117) = 1
LCM(10110,10117) = ( 10110 × 10117) / 1
LCM(10110,10117) = 102282870 / 1
LCM(10110,10117) = 102282870

(i) The LCM of 10117 and 10110 is associative

LCM of 10110 and 10117 = LCM of 10117 and 10110

1. What is the LCM of 10110 and 10117?

Answer: LCM of 10110 and 10117 is 102282870.

2. What are the Factors of 10110?

Answer: Factors of 10110 are 1, 2, 3, 5, 6, 10, 15, 30, 337, 674, 1011, 1685, 2022, 3370, 5055, 10110. There are 16 integers that are factors of 10110. The greatest factor of 10110 is 10110.

3. What are the Factors of 10117?

Answer: Factors of 10117 are 1, 67, 151, 10117. There are 4 integers that are factors of 10117. The greatest factor of 10117 is 10117.

4. How to Find the LCM of 10110 and 10117?

Answer:

Least Common Multiple of 10110 and 10117 = 102282870

Step 1: Find the prime factorization of 10110

10110 = 2 x 3 x 5 x 337

Step 2: Find the prime factorization of 10117

10117 = 67 x 151

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

LCM = 102282870 = 2 x 3 x 5 x 67 x 151 x 337

Step 4: Therefore, the least common multiple of 10110 and 10117 is 102282870.