Least Common Multiple of 31309 and 31314

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

• Least Common Multiple of 31309 and 31314 by Prime method
• Least Common Multiple of 31309 and 31314 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 31309 and 31314. First we will calculate the prime factors of 31309 and 31314.

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 31314

Prime factors of 31314 are 2, 3, 17,307. Prime factorization of 31314 in exponential form is:

31314 = 2¹×3¹×17¹×307¹

Now multiplying the highest exponent prime factors to calculate the LCM of 31309 and 31314.

LCM(31309,31314) = 2¹×3¹×17¹×131¹×239¹×307¹
LCM(31309,31314) = 980410026

Factors of 31309

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

1, 131, 239, 31309

Factors of 31314

List of positive integer factors of 31314 that divides 31314 without a remainder.

1, 2, 3, 6, 17, 34, 51, 102, 307, 614, 921, 1842, 5219, 10438, 15657, 31314

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31309 and 31314, than apply into the LCM equation.

GCF(31309,31314) = 1
LCM(31309,31314) = ( 31309 × 31314) / 1
LCM(31309,31314) = 980410026 / 1
LCM(31309,31314) = 980410026

(i) The LCM of 31314 and 31309 is associative

LCM of 31309 and 31314 = LCM of 31314 and 31309

1. What is the LCM of 31309 and 31314?

Answer: LCM of 31309 and 31314 is 980410026.

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 31314?

Answer: Factors of 31314 are 1, 2, 3, 6, 17, 34, 51, 102, 307, 614, 921, 1842, 5219, 10438, 15657, 31314. There are 16 integers that are factors of 31314. The greatest factor of 31314 is 31314.

4. How to Find the LCM of 31309 and 31314?

Answer:

Least Common Multiple of 31309 and 31314 = 980410026

Step 1: Find the prime factorization of 31309

31309 = 131 x 239

Step 2: Find the prime factorization of 31314

31314 = 2 x 3 x 17 x 307

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

LCM = 980410026 = 2 x 3 x 17 x 131 x 239 x 307

Step 4: Therefore, the least common multiple of 31309 and 31314 is 980410026.