Least Common Multiple of 31310 and 31318

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

• Least Common Multiple of 31310 and 31318 by Prime method
• Least Common Multiple of 31310 and 31318 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 31310 and 31318. First we will calculate the prime factors of 31310 and 31318.

Prime Factorization of 31310

Prime factors of 31310 are 2, 5, 31,101. Prime factorization of 31310 in exponential form is:

31310 = 2¹×5¹×31¹×101¹

Prime Factorization of 31318

Prime factors of 31318 are 2, 7,2237. Prime factorization of 31318 in exponential form is:

31318 = 2¹×7¹×2237¹

Now multiplying the highest exponent prime factors to calculate the LCM of 31310 and 31318.

LCM(31310,31318) = 2¹×5¹×7¹×31¹×101¹×2237¹
LCM(31310,31318) = 490283290

Factors of 31310

List of positive integer factors of 31310 that divides 31310 without a remainder.

1, 2, 5, 10, 31, 62, 101, 155, 202, 310, 505, 1010, 3131, 6262, 15655, 31310

Factors of 31318

List of positive integer factors of 31318 that divides 31318 without a remainder.

1, 2, 7, 14, 2237, 4474, 15659, 31318

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31310 and 31318, than apply into the LCM equation.

GCF(31310,31318) = 2
LCM(31310,31318) = ( 31310 × 31318) / 2
LCM(31310,31318) = 980566580 / 2
LCM(31310,31318) = 490283290

(i) The LCM of 31318 and 31310 is associative

LCM of 31310 and 31318 = LCM of 31318 and 31310

1. What is the LCM of 31310 and 31318?

Answer: LCM of 31310 and 31318 is 490283290.

2. What are the Factors of 31310?

Answer: Factors of 31310 are 1, 2, 5, 10, 31, 62, 101, 155, 202, 310, 505, 1010, 3131, 6262, 15655, 31310. There are 16 integers that are factors of 31310. The greatest factor of 31310 is 31310.

3. What are the Factors of 31318?

Answer: Factors of 31318 are 1, 2, 7, 14, 2237, 4474, 15659, 31318. There are 8 integers that are factors of 31318. The greatest factor of 31318 is 31318.

4. How to Find the LCM of 31310 and 31318?

Answer:

Least Common Multiple of 31310 and 31318 = 490283290

Step 1: Find the prime factorization of 31310

31310 = 2 x 5 x 31 x 101

Step 2: Find the prime factorization of 31318

31318 = 2 x 7 x 2237

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

LCM = 490283290 = 2 x 5 x 7 x 31 x 101 x 2237

Step 4: Therefore, the least common multiple of 31310 and 31318 is 490283290.