Given Numbers are 272, 280

We can find the LCM of 272, 280 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 272 and 280

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

Multiples of 280 =280,560,840,1120,1400,1680,1960,2240,2520,2800,3080,3360,3640,3920,4200,4480,4760,

Now, get the least common multiple of 272, 280 which is 9520

So, the LCM of 272, 280 is 9520.

One method for determining the LCM of 272 and 280 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 280's prime factorization:

Prime factors of 280 are 2, 5,7.

280 = 2³×5¹×7¹

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, 5,7

2⁴×5¹×7¹×17¹ = 9520

This shows that the LCM of 272 and 280 is 9520.

The first step in determining the Least Common Multiple of 272 and 280 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 272 and 280:

Lets look at the first ten multiples of these numbers, 272 and 280:

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

280,560,840,1120,1400,1680,1960,2240,2520,4760 are the first ten multiples of 280.

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 280, for example, are 3264, 4624, and 4480. 9520 is the least common multiple since it is the smallest.

272 and 280 have an LCM of 9520.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 272 and 280, than apply into the LCM equation.

GCF(272,280) = 8
LCM(272,280) = ( 272 × 280) / 8
LCM(272,280) = 76160 / 8
LCM(272,280) = 9520

1. What is the LCM of 272 and 280?

The LCM of 272 and 280 is 9520.

2. How to find the lowest common multiple of 272 and 280?

To find the lowest common multiple of 272 and 280, we have to get the multip;es of both numbers and identify the least common multiple in them which is 9520.

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 280?

Answer: Factors of 280 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280. There are 16 integers that are factors of 280. The greatest factor of 280 is 280.

Answer:

Least Common Multiple of 272 and 280 = 9520

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 280

280 = 2 x 2 x 2 x 5 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 = 9520 = 2 x 2 x 2 x 2 x 5 x 7 x 17

Step 4: Therefore, the least common multiple of 272 and 280 is 9520.