Least Common Multiple of 306 and 314

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 314 the smallest integer that is 48042 that is divisible by both numbers.

Least Common Multiple (LCM) of 306 and 314 is 48042.

LCM(306,314) = 48042

LCM of 306 and 314

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

LCM of:
and

Least Common Multiple of 306 and 314

LCM of 306 and 314 is 48042

Least common multiple can be found by multiplying the highest exponent prime factors of 306 and 314. First we will calculate the prime factors of 306 and 314.

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 314


2 314
157 157
1

Prime factors of 314 are 2,157. Prime factorization of 314 in exponential form is:

314 = 21×1571

Now multiplying the highest exponent prime factors to calculate the LCM of 306 and 314.

LCM(306,314) = 21×32×171×1571
LCM(306,314) = 48042

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 314

List of positive integer factors of 314 that divides 314 without a remainder.

1, 2, 157, 314

Least Common Multiple of 306 and 314 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 314, than apply into the LCM equation.

GCF(306,314) = 2
LCM(306,314) = ( 306 × 314) / 2
LCM(306,314) = 96084 / 2
LCM(306,314) = 48042

Properties of LCM 306 and 314

(i) The LCM of 314 and 306 is associative

LCM of 306 and 314 = LCM of 314 and 306

Related Least Common Multiples of 306

Related Least Common Multiples of 314

Frequently Asked Questions on LCM of 306 and 314

1. What is the LCM of 306 and 314?

Answer: LCM of 306 and 314 is 48042.

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 314?

Answer: Factors of 314 are 1, 2, 157, 314. There are 4 integers that are factors of 314. The greatest factor of 314 is 314.

4. How to Find the LCM of 306 and 314?

Answer:

Least Common Multiple of 306 and 314 = 48042

Step 1: Find the prime factorization of 306

306 = 2 x 3 x 3 x 17

Step 2: Find the prime factorization of 314

314 = 2 x 157

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

LCM = 48042 = 2 x 3 x 3 x 17 x 157

Step 4: Therefore, the least common multiple of 306 and 314 is 48042.