Given Numbers are 268, 272

We can find the LCM of 268, 272 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 268 and 272

Multiples of 268 =268,536,804,1072,1340,1608,1876,2144,2412,2680,2948,3216,3484,3752,4020,4288,4556,

Multiples of 272 =272,544,816,1088,1360,1632,1904,2176,2448,2720,2992,3264,3536,3808,4080,4352,4624,

Now, get the least common multiple of 268, 272 which is 18224

So, the LCM of 268, 272 is 18224.

One method for determining the LCM of 268 and 272 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 268's prime factorization:

Prime factors of 268 are 2,67.

268 = 2²×67¹

And this is 272's prime factorization:

Prime factors of 272 are 2,17.

272 = 2⁴×17¹

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: 2,67,17

2⁴×17¹×67¹ = 18224

This shows that the LCM of 268 and 272 is 18224.

The first step in determining the Least Common Multiple of 268 and 272 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 268 and 272:

Lets look at the first ten multiples of these numbers, 268 and 272:

268,536,804,1072,1340,1608,1876,2144,2412,4556 are the first ten multiples of 268.

272,544,816,1088,1360,1632,1904,2176,2448,4624 are the first ten multiples of 272.

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 268 and 272, for example, are 3216, 4556, and 4352. 18224 is the least common multiple since it is the smallest.

268 and 272 have an LCM of 18224.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 268 and 272, than apply into the LCM equation.

GCF(268,272) = 4
LCM(268,272) = ( 268 × 272) / 4
LCM(268,272) = 72896 / 4
LCM(268,272) = 18224

1. What is the LCM of 268 and 272?

The LCM of 268 and 272 is 18224.

2. How to find the lowest common multiple of 268 and 272?

To find the lowest common multiple of 268 and 272, we have to get the multip;es of both numbers and identify the least common multiple in them which is 18224.

3. What are the Factors of 268?

Answer: Factors of 268 are 1, 2, 4, 67, 134, 268. There are 6 integers that are factors of 268. The greatest factor of 268 is 268.

4. What are the Factors of 272?

Answer: Factors of 272 are 1, 2, 4, 8, 16, 17, 34, 68, 136, 272. There are 10 integers that are factors of 272. The greatest factor of 272 is 272.

Answer:

Least Common Multiple of 268 and 272 = 18224

Step 1: Find the prime factorization of 268

268 = 2 x 2 x 67

Step 2: Find the prime factorization of 272

272 = 2 x 2 x 2 x 2 x 17

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

LCM = 18224 = 2 x 2 x 2 x 2 x 17 x 67

Step 4: Therefore, the least common multiple of 268 and 272 is 18224.