Least Common Multiple of 305 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 305 and 312 the smallest integer that is 95160 that is divisible by both numbers.

Least Common Multiple (LCM) of 305 and 312 is 95160.

LCM(305,312) = 95160

LCM of 305 and 312

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

LCM of:
and

Least Common Multiple of 305 and 312

LCM of 305 and 312 is 95160

Least common multiple can be found by multiplying the highest exponent prime factors of 305 and 312. First we will calculate the prime factors of 305 and 312.

Prime Factorization of 305


5 305
61 61
1

Prime factors of 305 are 5,61. Prime factorization of 305 in exponential form is:

305 = 51×611

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 305 and 312.

LCM(305,312) = 23×31×51×131×611
LCM(305,312) = 95160

Factors of 305

List of positive integer factors of 305 that divides 305 without a remainder.

1, 5, 61, 305

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 305 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 305 and 312, than apply into the LCM equation.

GCF(305,312) = 1
LCM(305,312) = ( 305 × 312) / 1
LCM(305,312) = 95160 / 1
LCM(305,312) = 95160

Properties of LCM 305 and 312

(i) The LCM of 312 and 305 is associative

LCM of 305 and 312 = LCM of 312 and 305

Related Least Common Multiples of 305

Related Least Common Multiples of 312

Frequently Asked Questions on LCM of 305 and 312

1. What is the LCM of 305 and 312?

Answer: LCM of 305 and 312 is 95160.

2. What are the Factors of 305?

Answer: Factors of 305 are 1, 5, 61, 305. There are 4 integers that are factors of 305. The greatest factor of 305 is 305.

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 305 and 312?

Answer:

Least Common Multiple of 305 and 312 = 95160

Step 1: Find the prime factorization of 305

305 = 5 x 61

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 = 95160 = 2 x 2 x 2 x 3 x 5 x 13 x 61

Step 4: Therefore, the least common multiple of 305 and 312 is 95160.