Least Common Multiple of 314 and 315

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 314 and 315 the smallest integer that is 98910 that is divisible by both numbers.

Least Common Multiple (LCM) of 314 and 315 is 98910.

LCM(314,315) = 98910

LCM of 314 and 315

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

LCM of:
and

Least Common Multiple of 314 and 315

LCM of 314 and 315 is 98910

Least common multiple can be found by multiplying the highest exponent prime factors of 314 and 315. First we will calculate the prime factors of 314 and 315.

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

Prime Factorization of 315


3 315
3 105
5 35
7 7
1

Prime factors of 315 are 3, 5,7. Prime factorization of 315 in exponential form is:

315 = 32×51×71

Now multiplying the highest exponent prime factors to calculate the LCM of 314 and 315.

LCM(314,315) = 21×32×51×71×1571
LCM(314,315) = 98910

Factors of 314

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

1, 2, 157, 314

Factors of 315

List of positive integer factors of 315 that divides 315 without a remainder.

1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315

Least Common Multiple of 314 and 315 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 314 and 315, than apply into the LCM equation.

GCF(314,315) = 1
LCM(314,315) = ( 314 × 315) / 1
LCM(314,315) = 98910 / 1
LCM(314,315) = 98910

Properties of LCM 314 and 315

(i) The LCM of 315 and 314 is associative

LCM of 314 and 315 = LCM of 315 and 314

Related Least Common Multiples of 314

Related Least Common Multiples of 315

Frequently Asked Questions on LCM of 314 and 315

1. What is the LCM of 314 and 315?

Answer: LCM of 314 and 315 is 98910.

2. 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.

3. What are the Factors of 315?

Answer: Factors of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315. There are 12 integers that are factors of 315. The greatest factor of 315 is 315.

4. How to Find the LCM of 314 and 315?

Answer:

Least Common Multiple of 314 and 315 = 98910

Step 1: Find the prime factorization of 314

314 = 2 x 157

Step 2: Find the prime factorization of 315

315 = 3 x 3 x 5 x 7

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

LCM = 98910 = 2 x 3 x 3 x 5 x 7 x 157

Step 4: Therefore, the least common multiple of 314 and 315 is 98910.