Least Common Multiple of 306 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 306 and 310 the smallest integer that is 47430 that is divisible by both numbers.

Least Common Multiple (LCM) of 306 and 310 is 47430.

LCM(306,310) = 47430

LCM of 306 and 310

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

LCM of:
and

Least Common Multiple of 306 and 310

LCM of 306 and 310 is 47430

Least common multiple can be found by multiplying the highest exponent prime factors of 306 and 310. First we will calculate the prime factors of 306 and 310.

Prime Factorization of 306


2 306
3 153
3 51
17 17
1

Prime factors of 306 are 2, 3,17. Prime factorization of 306 in exponential form is:

306 = 21×32×171

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 306 and 310.

LCM(306,310) = 21×32×51×171×311
LCM(306,310) = 47430

Factors of 306

List of positive integer factors of 306 that divides 306 without a remainder.

1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306

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 306 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 306 and 310, than apply into the LCM equation.

GCF(306,310) = 2
LCM(306,310) = ( 306 × 310) / 2
LCM(306,310) = 94860 / 2
LCM(306,310) = 47430

Properties of LCM 306 and 310

(i) The LCM of 310 and 306 is associative

LCM of 306 and 310 = LCM of 310 and 306

Related Least Common Multiples of 306

Related Least Common Multiples of 310

Frequently Asked Questions on LCM of 306 and 310

1. What is the LCM of 306 and 310?

Answer: LCM of 306 and 310 is 47430.

2. What are the Factors of 306?

Answer: Factors of 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306. There are 12 integers that are factors of 306. The greatest factor of 306 is 306.

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 306 and 310?

Answer:

Least Common Multiple of 306 and 310 = 47430

Step 1: Find the prime factorization of 306

306 = 2 x 3 x 3 x 17

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 = 47430 = 2 x 3 x 3 x 5 x 17 x 31

Step 4: Therefore, the least common multiple of 306 and 310 is 47430.