Least Common Multiple of 31307 and 31314

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

• Least Common Multiple of 31307 and 31314 by Prime method
• Least Common Multiple of 31307 and 31314 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 31307 and 31314. First we will calculate the prime factors of 31307 and 31314.

Prime Factorization of 31307

Prime factors of 31307 are 31307. Prime factorization of 31307 in exponential form is:

31307 = 31307¹

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 31307 and 31314.

LCM(31307,31314) = 2¹×3¹×17¹×307¹×31307¹
LCM(31307,31314) = 980347398

Factors of 31307

List of positive integer factors of 31307 that divides 31307 without a remainder.

1, 31307

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 31307 and 31314, than apply into the LCM equation.

GCF(31307,31314) = 1
LCM(31307,31314) = ( 31307 × 31314) / 1
LCM(31307,31314) = 980347398 / 1
LCM(31307,31314) = 980347398

(i) The LCM of 31314 and 31307 is associative

LCM of 31307 and 31314 = LCM of 31314 and 31307

1. What is the LCM of 31307 and 31314?

Answer: LCM of 31307 and 31314 is 980347398.

2. What are the Factors of 31307?

Answer: Factors of 31307 are 1, 31307. There are 2 integers that are factors of 31307. The greatest factor of 31307 is 31307.

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 31307 and 31314?

Answer:

Least Common Multiple of 31307 and 31314 = 980347398

Step 1: Find the prime factorization of 31307

31307 = 31307

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 = 980347398 = 2 x 3 x 17 x 307 x 31307

Step 4: Therefore, the least common multiple of 31307 and 31314 is 980347398.