Least Common Multiple of 306 and 308

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 308 the smallest integer that is 47124 that is divisible by both numbers.

Least Common Multiple (LCM) of 306 and 308 is 47124.

LCM(306,308) = 47124

LCM of 306 and 308

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

LCM of:
and

Least Common Multiple of 306 and 308

LCM of 306 and 308 is 47124

Least common multiple can be found by multiplying the highest exponent prime factors of 306 and 308. First we will calculate the prime factors of 306 and 308.

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 308


2 308
2 154
7 77
11 11
1

Prime factors of 308 are 2, 7,11. Prime factorization of 308 in exponential form is:

308 = 22×71×111

Now multiplying the highest exponent prime factors to calculate the LCM of 306 and 308.

LCM(306,308) = 22×32×71×111×171
LCM(306,308) = 47124

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 308

List of positive integer factors of 308 that divides 308 without a remainder.

1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308

Least Common Multiple of 306 and 308 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 308, than apply into the LCM equation.

GCF(306,308) = 2
LCM(306,308) = ( 306 × 308) / 2
LCM(306,308) = 94248 / 2
LCM(306,308) = 47124

Properties of LCM 306 and 308

(i) The LCM of 308 and 306 is associative

LCM of 306 and 308 = LCM of 308 and 306

Related Least Common Multiples of 306

Related Least Common Multiples of 308

Frequently Asked Questions on LCM of 306 and 308

1. What is the LCM of 306 and 308?

Answer: LCM of 306 and 308 is 47124.

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 308?

Answer: Factors of 308 are 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308. There are 12 integers that are factors of 308. The greatest factor of 308 is 308.

4. How to Find the LCM of 306 and 308?

Answer:

Least Common Multiple of 306 and 308 = 47124

Step 1: Find the prime factorization of 306

306 = 2 x 3 x 3 x 17

Step 2: Find the prime factorization of 308

308 = 2 x 2 x 7 x 11

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

LCM = 47124 = 2 x 2 x 3 x 3 x 7 x 11 x 17

Step 4: Therefore, the least common multiple of 306 and 308 is 47124.