Least Common Multiple of 31310 and 31314

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 31310 and 31314 the smallest integer that is 490220670 that is divisible by both numbers.

Least Common Multiple (LCM) of 31310 and 31314 is 490220670.

LCM(31310,31314) = 490220670

LCM of 31310 and 31314

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

LCM of:
and

Least Common Multiple of 31310 and 31314

LCM of 31310 and 31314 is 490220670

Least common multiple can be found by multiplying the highest exponent prime factors of 31310 and 31314. First we will calculate the prime factors of 31310 and 31314.

Prime Factorization of 31310


2 31310
5 15655
31 3131
101 101
1

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 31314


2 31314
3 15657
17 5219
307 307
1

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 31310 and 31314.

LCM(31310,31314) = 21×31×51×171×311×1011×3071
LCM(31310,31314) = 490220670

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 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

Least Common Multiple of 31310 and 31314 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31310 and 31314, than apply into the LCM equation.

GCF(31310,31314) = 2
LCM(31310,31314) = ( 31310 × 31314) / 2
LCM(31310,31314) = 980441340 / 2
LCM(31310,31314) = 490220670

Properties of LCM 31310 and 31314

(i) The LCM of 31314 and 31310 is associative

LCM of 31310 and 31314 = LCM of 31314 and 31310

Related Least Common Multiples of 31310

Related Least Common Multiples of 31314

Frequently Asked Questions on LCM of 31310 and 31314

1. What is the LCM of 31310 and 31314?

Answer: LCM of 31310 and 31314 is 490220670.

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 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 31310 and 31314?

Answer:

Least Common Multiple of 31310 and 31314 = 490220670

Step 1: Find the prime factorization of 31310

31310 = 2 x 5 x 31 x 101

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 = 490220670 = 2 x 3 x 5 x 17 x 31 x 101 x 307

Step 4: Therefore, the least common multiple of 31310 and 31314 is 490220670.