Least Common Multiple of 31309 and 31317

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

• Least Common Multiple of 31309 and 31317 by Prime method
• Least Common Multiple of 31309 and 31317 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 31309 and 31317. First we will calculate the prime factors of 31309 and 31317.

Prime Factorization of 31309

Prime factors of 31309 are 131,239. Prime factorization of 31309 in exponential form is:

31309 = 131¹×239¹

Prime Factorization of 31317

Prime factors of 31317 are 3, 11, 13,73. Prime factorization of 31317 in exponential form is:

31317 = 3¹×11¹×13¹×73¹

Now multiplying the highest exponent prime factors to calculate the LCM of 31309 and 31317.

LCM(31309,31317) = 3¹×11¹×13¹×73¹×131¹×239¹
LCM(31309,31317) = 980503953

Factors of 31309

List of positive integer factors of 31309 that divides 31309 without a remainder.

1, 131, 239, 31309

Factors of 31317

List of positive integer factors of 31317 that divides 31317 without a remainder.

1, 3, 11, 13, 33, 39, 73, 143, 219, 429, 803, 949, 2409, 2847, 10439, 31317

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31309 and 31317, than apply into the LCM equation.

GCF(31309,31317) = 1
LCM(31309,31317) = ( 31309 × 31317) / 1
LCM(31309,31317) = 980503953 / 1
LCM(31309,31317) = 980503953

(i) The LCM of 31317 and 31309 is associative

LCM of 31309 and 31317 = LCM of 31317 and 31309

1. What is the LCM of 31309 and 31317?

Answer: LCM of 31309 and 31317 is 980503953.

2. What are the Factors of 31309?

Answer: Factors of 31309 are 1, 131, 239, 31309. There are 4 integers that are factors of 31309. The greatest factor of 31309 is 31309.

3. What are the Factors of 31317?

Answer: Factors of 31317 are 1, 3, 11, 13, 33, 39, 73, 143, 219, 429, 803, 949, 2409, 2847, 10439, 31317. There are 16 integers that are factors of 31317. The greatest factor of 31317 is 31317.

4. How to Find the LCM of 31309 and 31317?

Answer:

Least Common Multiple of 31309 and 31317 = 980503953

Step 1: Find the prime factorization of 31309

31309 = 131 x 239

Step 2: Find the prime factorization of 31317

31317 = 3 x 11 x 13 x 73

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

LCM = 980503953 = 3 x 11 x 13 x 73 x 131 x 239

Step 4: Therefore, the least common multiple of 31309 and 31317 is 980503953.