Given Numbers are 289, 294

We can find the LCM of 289, 294 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 289 and 294

Multiples of 289 =289,578,867,1156,1445,1734,2023,2312,2601,2890,3179,3468,3757,4046,4335,4624,4913,

Multiples of 294 =294,588,882,1176,1470,1764,2058,2352,2646,2940,3234,3528,3822,4116,4410,4704,4998,

Now, get the least common multiple of 289, 294 which is 84966

So, the LCM of 289, 294 is 84966.

One method for determining the LCM of 289 and 294 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 289's prime factorization:

Prime factors of 289 are 17.

289 = 17²

And this is 294's prime factorization:

Prime factors of 294 are 2, 3,7.

294 = 2¹×3¹×7²

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:17, 2, 3,7

2¹×3¹×7²×17² = 84966

This shows that the LCM of 289 and 294 is 84966.

The first step in determining the Least Common Multiple of 289 and 294 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 289 and 294:

Lets look at the first ten multiples of these numbers, 289 and 294:

289,578,867,1156,1445,1734,2023,2312,2601,4913 are the first ten multiples of 289.

294,588,882,1176,1470,1764,2058,2352,2646,4998 are the first ten multiples of 294.

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 289 and 294, for example, are 3468, 4913, and 4704. 84966 is the least common multiple since it is the smallest.

289 and 294 have an LCM of 84966.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 289 and 294, than apply into the LCM equation.

GCF(289,294) = 1
LCM(289,294) = ( 289 × 294) / 1
LCM(289,294) = 84966 / 1
LCM(289,294) = 84966

1. What is the LCM of 289 and 294?

The LCM of 289 and 294 is 84966.

2. How to find the lowest common multiple of 289 and 294?

To find the lowest common multiple of 289 and 294, we have to get the multip;es of both numbers and identify the least common multiple in them which is 84966.

3. What are the Factors of 289?

Answer: Factors of 289 are 1, 17, 289. There are 3 integers that are factors of 289. The greatest factor of 289 is 289.

4. What are the Factors of 294?

Answer: Factors of 294 are 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294. There are 12 integers that are factors of 294. The greatest factor of 294 is 294.

Answer:

Least Common Multiple of 289 and 294 = 84966

Step 1: Find the prime factorization of 289

289 = 17 x 17

Step 2: Find the prime factorization of 294

294 = 2 x 3 x 7 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 = 84966 = 2 x 3 x 7 x 7 x 17 x 17

Step 4: Therefore, the least common multiple of 289 and 294 is 84966.