Given Numbers are 272, 278

We can find the LCM of 272, 278 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 272 and 278

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

Multiples of 278 =278,556,834,1112,1390,1668,1946,2224,2502,2780,3058,3336,3614,3892,4170,4448,4726,

Now, get the least common multiple of 272, 278 which is 37808

So, the LCM of 272, 278 is 37808.

One method for determining the LCM of 272 and 278 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 272's prime factorization:

Prime factors of 272 are 2,17.

272 = 2⁴×17¹

And this is 278's prime factorization:

Prime factors of 278 are 2,139.

278 = 2¹×139¹

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: 2,17,139

2⁴×17¹×139¹ = 37808

This shows that the LCM of 272 and 278 is 37808.

The first step in determining the Least Common Multiple of 272 and 278 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 272 and 278:

Lets look at the first ten multiples of these numbers, 272 and 278:

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

278,556,834,1112,1390,1668,1946,2224,2502,4726 are the first ten multiples of 278.

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 272 and 278, for example, are 3264, 4624, and 4448. 37808 is the least common multiple since it is the smallest.

272 and 278 have an LCM of 37808.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 272 and 278, than apply into the LCM equation.

GCF(272,278) = 2
LCM(272,278) = ( 272 × 278) / 2
LCM(272,278) = 75616 / 2
LCM(272,278) = 37808

1. What is the LCM of 272 and 278?

The LCM of 272 and 278 is 37808.

2. How to find the lowest common multiple of 272 and 278?

To find the lowest common multiple of 272 and 278, we have to get the multip;es of both numbers and identify the least common multiple in them which is 37808.

3. 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.

4. What are the Factors of 278?

Answer: Factors of 278 are 1, 2, 139, 278. There are 4 integers that are factors of 278. The greatest factor of 278 is 278.

Answer:

Least Common Multiple of 272 and 278 = 37808

Step 1: Find the prime factorization of 272

272 = 2 x 2 x 2 x 2 x 17

Step 2: Find the prime factorization of 278

278 = 2 x 139

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

LCM = 37808 = 2 x 2 x 2 x 2 x 17 x 139

Step 4: Therefore, the least common multiple of 272 and 278 is 37808.