Least Common Multiple of 312 and 319

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 312 and 319 the smallest integer that is 99528 that is divisible by both numbers.

Least Common Multiple (LCM) of 312 and 319 is 99528.

LCM(312,319) = 99528

LCM of 312 and 319

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

LCM of:
and

Least Common Multiple of 312 and 319

LCM of 312 and 319 is 99528

Least common multiple can be found by multiplying the highest exponent prime factors of 312 and 319. First we will calculate the prime factors of 312 and 319.

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

Prime Factorization of 319


11 319
29 29
1

Prime factors of 319 are 11,29. Prime factorization of 319 in exponential form is:

319 = 111×291

Now multiplying the highest exponent prime factors to calculate the LCM of 312 and 319.

LCM(312,319) = 23×31×111×131×291
LCM(312,319) = 99528

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

Factors of 319

List of positive integer factors of 319 that divides 319 without a remainder.

1, 11, 29, 319

Least Common Multiple of 312 and 319 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 312 and 319, than apply into the LCM equation.

GCF(312,319) = 1
LCM(312,319) = ( 312 × 319) / 1
LCM(312,319) = 99528 / 1
LCM(312,319) = 99528

Properties of LCM 312 and 319

(i) The LCM of 319 and 312 is associative

LCM of 312 and 319 = LCM of 319 and 312

Related Least Common Multiples of 312

Related Least Common Multiples of 319

Frequently Asked Questions on LCM of 312 and 319

1. What is the LCM of 312 and 319?

Answer: LCM of 312 and 319 is 99528.

2. 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.

3. What are the Factors of 319?

Answer: Factors of 319 are 1, 11, 29, 319. There are 4 integers that are factors of 319. The greatest factor of 319 is 319.

4. How to Find the LCM of 312 and 319?

Answer:

Least Common Multiple of 312 and 319 = 99528

Step 1: Find the prime factorization of 312

312 = 2 x 2 x 2 x 3 x 13

Step 2: Find the prime factorization of 319

319 = 11 x 29

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

LCM = 99528 = 2 x 2 x 2 x 3 x 11 x 13 x 29

Step 4: Therefore, the least common multiple of 312 and 319 is 99528.