Least Common Multiple of 314 and 316

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 316 the smallest integer that is 49612 that is divisible by both numbers.

Least Common Multiple (LCM) of 314 and 316 is 49612.

LCM(314,316) = 49612

LCM of 314 and 316

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

LCM of:
and

Least Common Multiple of 314 and 316

LCM of 314 and 316 is 49612

Least common multiple can be found by multiplying the highest exponent prime factors of 314 and 316. First we will calculate the prime factors of 314 and 316.

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 316


2 316
2 158
79 79
1

Prime factors of 316 are 2,79. Prime factorization of 316 in exponential form is:

316 = 22×791

Now multiplying the highest exponent prime factors to calculate the LCM of 314 and 316.

LCM(314,316) = 22×791×1571
LCM(314,316) = 49612

Factors of 314

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

1, 2, 157, 314

Factors of 316

List of positive integer factors of 316 that divides 316 without a remainder.

1, 2, 4, 79, 158, 316

Least Common Multiple of 314 and 316 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 316, than apply into the LCM equation.

GCF(314,316) = 2
LCM(314,316) = ( 314 × 316) / 2
LCM(314,316) = 99224 / 2
LCM(314,316) = 49612

Properties of LCM 314 and 316

(i) The LCM of 316 and 314 is associative

LCM of 314 and 316 = LCM of 316 and 314

Related Least Common Multiples of 314

Related Least Common Multiples of 316

Frequently Asked Questions on LCM of 314 and 316

1. What is the LCM of 314 and 316?

Answer: LCM of 314 and 316 is 49612.

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 316?

Answer: Factors of 316 are 1, 2, 4, 79, 158, 316. There are 6 integers that are factors of 316. The greatest factor of 316 is 316.

4. How to Find the LCM of 314 and 316?

Answer:

Least Common Multiple of 314 and 316 = 49612

Step 1: Find the prime factorization of 314

314 = 2 x 157

Step 2: Find the prime factorization of 316

316 = 2 x 2 x 79

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

LCM = 49612 = 2 x 2 x 79 x 157

Step 4: Therefore, the least common multiple of 314 and 316 is 49612.