Given Numbers are 49, 56

We can find the LCM of 49, 56 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 49 and 56

Multiples of 49 =49,98,147,196,245,294,343,392,441,490,539,588,637,686,735,784,833,

Multiples of 56 =56,112,168,224,280,336,392,448,504,560,616,672,728,784,840,896,952,

Now, get the least common multiple of 49, 56 which is 392

So, the LCM of 49, 56 is 392.

One method for determining the LCM of 49 and 56 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 49's prime factorization:

Prime factors of 49 are 7.

49 = 7²

And this is 56's prime factorization:

Prime factors of 56 are 2,7.

56 = 2³×7¹

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:7,2

2³×7² = 392

This shows that the LCM of 49 and 56 is 392.

The first step in determining the Least Common Multiple of 49 and 56 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 49 and 56:

Lets look at the first ten multiples of these numbers, 49 and 56:

49,98,147,196,245,294,343,392,441,833 are the first ten multiples of 49.

56,112,168,224,280,336,392,448,504,952 are the first ten multiples of 56.

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 49 and 56, for example, are 588, 833, and 896. 392 is the least common multiple since it is the smallest.

49 and 56 have an LCM of 392.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 49 and 56, than apply into the LCM equation.

GCF(49,56) = 7
LCM(49,56) = ( 49 × 56) / 7
LCM(49,56) = 2744 / 7
LCM(49,56) = 392

1. What is the LCM of 49 and 56?

The LCM of 49 and 56 is 392.

2. How to find the lowest common multiple of 49 and 56?

To find the lowest common multiple of 49 and 56, we have to get the multip;es of both numbers and identify the least common multiple in them which is 392.

3. What are the Factors of 49?

Answer: Factors of 49 are 1, 7, 49. There are 3 integers that are factors of 49. The greatest factor of 49 is 49.

4. What are the Factors of 56?

Answer: Factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56. There are 8 integers that are factors of 56. The greatest factor of 56 is 56.

Answer:

Least Common Multiple of 49 and 56 = 392

Step 1: Find the prime factorization of 49

49 = 7 x 7

Step 2: Find the prime factorization of 56

56 = 2 x 2 x 2 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 = 392 = 2 x 2 x 2 x 7 x 7

Step 4: Therefore, the least common multiple of 49 and 56 is 392.