Least Common Multiple of 305 and 306

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 306 the smallest integer that is 93330 that is divisible by both numbers.

Least Common Multiple (LCM) of 305 and 306 is 93330.

LCM(305,306) = 93330

LCM of 305 and 306

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

LCM of:
and

Least Common Multiple of 305 and 306

LCM of 305 and 306 is 93330

Least common multiple can be found by multiplying the highest exponent prime factors of 305 and 306. First we will calculate the prime factors of 305 and 306.

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 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

Now multiplying the highest exponent prime factors to calculate the LCM of 305 and 306.

LCM(305,306) = 21×32×51×171×611
LCM(305,306) = 93330

Factors of 305

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

1, 5, 61, 305

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

Least Common Multiple of 305 and 306 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 306, than apply into the LCM equation.

GCF(305,306) = 1
LCM(305,306) = ( 305 × 306) / 1
LCM(305,306) = 93330 / 1
LCM(305,306) = 93330

Properties of LCM 305 and 306

(i) The LCM of 306 and 305 is associative

LCM of 305 and 306 = LCM of 306 and 305

Related Least Common Multiples of 305

Related Least Common Multiples of 306

Frequently Asked Questions on LCM of 305 and 306

1. What is the LCM of 305 and 306?

Answer: LCM of 305 and 306 is 93330.

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 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.

4. How to Find the LCM of 305 and 306?

Answer:

Least Common Multiple of 305 and 306 = 93330

Step 1: Find the prime factorization of 305

305 = 5 x 61

Step 2: Find the prime factorization of 306

306 = 2 x 3 x 3 x 17

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

LCM = 93330 = 2 x 3 x 3 x 5 x 17 x 61

Step 4: Therefore, the least common multiple of 305 and 306 is 93330.