Least Common Multiple of 10217 and 10218

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

• Least Common Multiple of 10217 and 10218 by Prime method
• Least Common Multiple of 10217 and 10218 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 10217 and 10218. First we will calculate the prime factors of 10217 and 10218.

Prime Factorization of 10217

Prime factors of 10217 are 17,601. Prime factorization of 10217 in exponential form is:

10217 = 17¹×601¹

Prime Factorization of 10218

Prime factors of 10218 are 2, 3, 13,131. Prime factorization of 10218 in exponential form is:

10218 = 2¹×3¹×13¹×131¹

Now multiplying the highest exponent prime factors to calculate the LCM of 10217 and 10218.

LCM(10217,10218) = 2¹×3¹×13¹×17¹×131¹×601¹
LCM(10217,10218) = 104397306

Factors of 10217

List of positive integer factors of 10217 that divides 10217 without a remainder.

1, 17, 601, 10217

Factors of 10218

List of positive integer factors of 10218 that divides 10218 without a remainder.

1, 2, 3, 6, 13, 26, 39, 78, 131, 262, 393, 786, 1703, 3406, 5109, 10218

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10217 and 10218, than apply into the LCM equation.

GCF(10217,10218) = 1
LCM(10217,10218) = ( 10217 × 10218) / 1
LCM(10217,10218) = 104397306 / 1
LCM(10217,10218) = 104397306

(i) The LCM of 10218 and 10217 is associative

LCM of 10217 and 10218 = LCM of 10218 and 10217

1. What is the LCM of 10217 and 10218?

Answer: LCM of 10217 and 10218 is 104397306.

2. What are the Factors of 10217?

Answer: Factors of 10217 are 1, 17, 601, 10217. There are 4 integers that are factors of 10217. The greatest factor of 10217 is 10217.

3. What are the Factors of 10218?

Answer: Factors of 10218 are 1, 2, 3, 6, 13, 26, 39, 78, 131, 262, 393, 786, 1703, 3406, 5109, 10218. There are 16 integers that are factors of 10218. The greatest factor of 10218 is 10218.

4. How to Find the LCM of 10217 and 10218?

Answer:

Least Common Multiple of 10217 and 10218 = 104397306

Step 1: Find the prime factorization of 10217

10217 = 17 x 601

Step 2: Find the prime factorization of 10218

10218 = 2 x 3 x 13 x 131

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

LCM = 104397306 = 2 x 3 x 13 x 17 x 131 x 601

Step 4: Therefore, the least common multiple of 10217 and 10218 is 104397306.