Least Common Multiple of 31314 and 31319

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

• Least Common Multiple of 31314 and 31319 by Prime method
• Least Common Multiple of 31314 and 31319 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 31314 and 31319. First we will calculate the prime factors of 31314 and 31319.

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

Prime Factorization of 31319

Prime factors of 31319 are 31319. Prime factorization of 31319 in exponential form is:

31319 = 31319¹

Now multiplying the highest exponent prime factors to calculate the LCM of 31314 and 31319.

LCM(31314,31319) = 2¹×3¹×17¹×307¹×31319¹
LCM(31314,31319) = 980723166

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

Factors of 31319

List of positive integer factors of 31319 that divides 31319 without a remainder.

1, 31319

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31314 and 31319, than apply into the LCM equation.

GCF(31314,31319) = 1
LCM(31314,31319) = ( 31314 × 31319) / 1
LCM(31314,31319) = 980723166 / 1
LCM(31314,31319) = 980723166

(i) The LCM of 31319 and 31314 is associative

LCM of 31314 and 31319 = LCM of 31319 and 31314

1. What is the LCM of 31314 and 31319?

Answer: LCM of 31314 and 31319 is 980723166.

2. 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.

3. What are the Factors of 31319?

Answer: Factors of 31319 are 1, 31319. There are 2 integers that are factors of 31319. The greatest factor of 31319 is 31319.

4. How to Find the LCM of 31314 and 31319?

Answer:

Least Common Multiple of 31314 and 31319 = 980723166

Step 1: Find the prime factorization of 31314

31314 = 2 x 3 x 17 x 307

Step 2: Find the prime factorization of 31319

31319 = 31319

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

LCM = 980723166 = 2 x 3 x 17 x 307 x 31319

Step 4: Therefore, the least common multiple of 31314 and 31319 is 980723166.