Given Numbers are 289, 296

We can find the LCM of 289, 296 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 289 and 296

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

Multiples of 296 =296,592,888,1184,1480,1776,2072,2368,2664,2960,3256,3552,3848,4144,4440,4736,5032,

Now, get the least common multiple of 289, 296 which is 85544

So, the LCM of 289, 296 is 85544.

One method for determining the LCM of 289 and 296 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 296's prime factorization:

Prime factors of 296 are 2,37.

296 = 2³×37¹

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, 2,37

2³×17²×37¹ = 85544

This shows that the LCM of 289 and 296 is 85544.

The first step in determining the Least Common Multiple of 289 and 296 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 289 and 296:

Lets look at the first ten multiples of these numbers, 289 and 296:

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

296,592,888,1184,1480,1776,2072,2368,2664,5032 are the first ten multiples of 296.

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 296, for example, are 3468, 4913, and 4736. 85544 is the least common multiple since it is the smallest.

289 and 296 have an LCM of 85544.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 289 and 296, than apply into the LCM equation.

GCF(289,296) = 1
LCM(289,296) = ( 289 × 296) / 1
LCM(289,296) = 85544 / 1
LCM(289,296) = 85544

1. What is the LCM of 289 and 296?

The LCM of 289 and 296 is 85544.

2. How to find the lowest common multiple of 289 and 296?

To find the lowest common multiple of 289 and 296, we have to get the multip;es of both numbers and identify the least common multiple in them which is 85544.

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 296?

Answer: Factors of 296 are 1, 2, 4, 8, 37, 74, 148, 296. There are 8 integers that are factors of 296. The greatest factor of 296 is 296.

Answer:

Least Common Multiple of 289 and 296 = 85544

Step 1: Find the prime factorization of 289

289 = 17 x 17

Step 2: Find the prime factorization of 296

296 = 2 x 2 x 2 x 37

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

LCM = 85544 = 2 x 2 x 2 x 17 x 17 x 37

Step 4: Therefore, the least common multiple of 289 and 296 is 85544.