Least Common Multiple of 305 and 310

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 310 the smallest integer that is 18910 that is divisible by both numbers.

Least Common Multiple (LCM) of 305 and 310 is 18910.

LCM(305,310) = 18910

LCM of 305 and 310

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

LCM of:
and

Least Common Multiple of 305 and 310

LCM of 305 and 310 is 18910

Least common multiple can be found by multiplying the highest exponent prime factors of 305 and 310. First we will calculate the prime factors of 305 and 310.

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 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

Now multiplying the highest exponent prime factors to calculate the LCM of 305 and 310.

LCM(305,310) = 21×51×311×611
LCM(305,310) = 18910

Factors of 305

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

1, 5, 61, 305

Factors of 310

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

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

Least Common Multiple of 305 and 310 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 310, than apply into the LCM equation.

GCF(305,310) = 5
LCM(305,310) = ( 305 × 310) / 5
LCM(305,310) = 94550 / 5
LCM(305,310) = 18910

Properties of LCM 305 and 310

(i) The LCM of 310 and 305 is associative

LCM of 305 and 310 = LCM of 310 and 305

Related Least Common Multiples of 305

Related Least Common Multiples of 310

Frequently Asked Questions on LCM of 305 and 310

1. What is the LCM of 305 and 310?

Answer: LCM of 305 and 310 is 18910.

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 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.

4. How to Find the LCM of 305 and 310?

Answer:

Least Common Multiple of 305 and 310 = 18910

Step 1: Find the prime factorization of 305

305 = 5 x 61

Step 2: Find the prime factorization of 310

310 = 2 x 5 x 31

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

LCM = 18910 = 2 x 5 x 31 x 61

Step 4: Therefore, the least common multiple of 305 and 310 is 18910.