Least Common Multiple of 9309 and 9310

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

• Least Common Multiple of 9309 and 9310 by Prime method
• Least Common Multiple of 9309 and 9310 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 9309 and 9310. First we will calculate the prime factors of 9309 and 9310.

Prime Factorization of 9309

Prime factors of 9309 are 3, 29,107. Prime factorization of 9309 in exponential form is:

9309 = 3¹×29¹×107¹

Prime Factorization of 9310

Prime factors of 9310 are 2, 5, 7,19. Prime factorization of 9310 in exponential form is:

9310 = 2¹×5¹×7²×19¹

Now multiplying the highest exponent prime factors to calculate the LCM of 9309 and 9310.

LCM(9309,9310) = 2¹×3¹×5¹×7²×19¹×29¹×107¹
LCM(9309,9310) = 86666790

Factors of 9309

List of positive integer factors of 9309 that divides 9309 without a remainder.

1, 3, 29, 87, 107, 321, 3103, 9309

Factors of 9310

List of positive integer factors of 9310 that divides 9310 without a remainder.

1, 2, 5, 7, 10, 14, 19, 35, 38, 49, 70, 95, 98, 133, 190, 245, 266, 490, 665, 931, 1330, 1862, 4655, 9310

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9309 and 9310, than apply into the LCM equation.

GCF(9309,9310) = 1
LCM(9309,9310) = ( 9309 × 9310) / 1
LCM(9309,9310) = 86666790 / 1
LCM(9309,9310) = 86666790

(i) The LCM of 9310 and 9309 is associative

LCM of 9309 and 9310 = LCM of 9310 and 9309

1. What is the LCM of 9309 and 9310?

Answer: LCM of 9309 and 9310 is 86666790.

2. What are the Factors of 9309?

Answer: Factors of 9309 are 1, 3, 29, 87, 107, 321, 3103, 9309. There are 8 integers that are factors of 9309. The greatest factor of 9309 is 9309.

3. What are the Factors of 9310?

Answer: Factors of 9310 are 1, 2, 5, 7, 10, 14, 19, 35, 38, 49, 70, 95, 98, 133, 190, 245, 266, 490, 665, 931, 1330, 1862, 4655, 9310. There are 24 integers that are factors of 9310. The greatest factor of 9310 is 9310.

4. How to Find the LCM of 9309 and 9310?

Answer:

Least Common Multiple of 9309 and 9310 = 86666790

Step 1: Find the prime factorization of 9309

9309 = 3 x 29 x 107

Step 2: Find the prime factorization of 9310

9310 = 2 x 5 x 7 x 7 x 19

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

LCM = 86666790 = 2 x 3 x 5 x 7 x 7 x 19 x 29 x 107

Step 4: Therefore, the least common multiple of 9309 and 9310 is 86666790.