Least Common Multiple of 310 and 312

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 310 and 312 the smallest integer that is 48360 that is divisible by both numbers.

Least Common Multiple (LCM) of 310 and 312 is 48360.

LCM(310,312) = 48360

LCM of 310 and 312

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

LCM of:
and

Least Common Multiple of 310 and 312

LCM of 310 and 312 is 48360

Least common multiple can be found by multiplying the highest exponent prime factors of 310 and 312. First we will calculate the prime factors of 310 and 312.

Prime Factorization of 310


2 310
5 155
31 31
1

Prime factors of 310 are 2, 5,31. Prime factorization of 310 in exponential form is:

310 = 21×51×311

Prime Factorization of 312


2 312
2 156
2 78
3 39
13 13
1

Prime factors of 312 are 2, 3,13. Prime factorization of 312 in exponential form is:

312 = 23×31×131

Now multiplying the highest exponent prime factors to calculate the LCM of 310 and 312.

LCM(310,312) = 23×31×51×131×311
LCM(310,312) = 48360

Factors of 310

List of positive integer factors of 310 that divides 310 without a remainder.

1, 2, 5, 10, 31, 62, 155, 310

Factors of 312

List of positive integer factors of 312 that divides 312 without a remainder.

1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312

Least Common Multiple of 310 and 312 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 310 and 312, than apply into the LCM equation.

GCF(310,312) = 2
LCM(310,312) = ( 310 × 312) / 2
LCM(310,312) = 96720 / 2
LCM(310,312) = 48360

Properties of LCM 310 and 312

(i) The LCM of 312 and 310 is associative

LCM of 310 and 312 = LCM of 312 and 310

Related Least Common Multiples of 310

Related Least Common Multiples of 312

Frequently Asked Questions on LCM of 310 and 312

1. What is the LCM of 310 and 312?

Answer: LCM of 310 and 312 is 48360.

2. What are the Factors of 310?

Answer: Factors of 310 are 1, 2, 5, 10, 31, 62, 155, 310. There are 8 integers that are factors of 310. The greatest factor of 310 is 310.

3. What are the Factors of 312?

Answer: Factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312. There are 16 integers that are factors of 312. The greatest factor of 312 is 312.

4. How to Find the LCM of 310 and 312?

Answer:

Least Common Multiple of 310 and 312 = 48360

Step 1: Find the prime factorization of 310

310 = 2 x 5 x 31

Step 2: Find the prime factorization of 312

312 = 2 x 2 x 2 x 3 x 13

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

LCM = 48360 = 2 x 2 x 2 x 3 x 5 x 13 x 31

Step 4: Therefore, the least common multiple of 310 and 312 is 48360.