Given Numbers are 309, 316

We can find the LCM of 309, 316 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 309 and 316

Multiples of 309 =309,618,927,1236,1545,1854,2163,2472,2781,3090,3399,3708,4017,4326,4635,4944,5253,

Multiples of 316 =316,632,948,1264,1580,1896,2212,2528,2844,3160,3476,3792,4108,4424,4740,5056,5372,

Now, get the least common multiple of 309, 316 which is 97644

So, the LCM of 309, 316 is 97644.

One method for determining the LCM of 309 and 316 is to compare the prime factorization of each number. You can find the prime factorization for each number by following the instructions below:

Here is 309's prime factorization:

Prime factors of 309 are 3,103.

309 = 3¹×103¹

And this is 316's prime factorization:

Prime factors of 316 are 2,79.

316 = 2²×79¹

When comparing the prime factorization of these two numbers, look for the highest power to which each prime factor is raised. In this case, the following primary factors must be considered: 3,103, 2,79

2²×3¹×79¹×103¹ = 97644

This shows that the LCM of 309 and 316 is 97644.

The first step in determining the Least Common Multiple of 309 and 316 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 309 and 316:

Lets look at the first ten multiples of these numbers, 309 and 316:

309,618,927,1236,1545,1854,2163,2472,2781,5253 are the first ten multiples of 309.

316,632,948,1264,1580,1896,2212,2528,2844,5372 are the first ten multiples of 316.

You can continue to list the multiples of these numbers until you find a match. Once you have found a match, or several matches, the Least Common Multiple is the smallest of these matches. The first matching multiple(s) of 309 and 316, for example, are 3708, 5253, and 5056. 97644 is the least common multiple since it is the smallest.

309 and 316 have an LCM of 97644.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 309 and 316, than apply into the LCM equation.

GCF(309,316) = 1
LCM(309,316) = ( 309 × 316) / 1
LCM(309,316) = 97644 / 1
LCM(309,316) = 97644

1. What is the LCM of 309 and 316?

The LCM of 309 and 316 is 97644.

2. How to find the lowest common multiple of 309 and 316?

To find the lowest common multiple of 309 and 316, we have to get the multip;es of both numbers and identify the least common multiple in them which is 97644.

3. What are the Factors of 309?

Answer: Factors of 309 are 1, 3, 103, 309. There are 4 integers that are factors of 309. The greatest factor of 309 is 309.

4. 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.

Answer:

Least Common Multiple of 309 and 316 = 97644

Step 1: Find the prime factorization of 309

309 = 3 x 103

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 = 97644 = 2 x 2 x 3 x 79 x 103

Step 4: Therefore, the least common multiple of 309 and 316 is 97644.