Given Numbers are 5760, 5766

We can find the LCM of 5760, 5766 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 5760 and 5766

Multiples of 5760 =5760,11520,17280,23040,28800,34560,40320,46080,51840,57600,63360,69120,74880,80640,86400,92160,97920,

Multiples of 5766 =5766,11532,17298,23064,28830,34596,40362,46128,51894,57660,63426,69192,74958,80724,86490,92256,98022,

Now, get the least common multiple of 5760, 5766 which is 5535360

So, the LCM of 5760, 5766 is 5535360.

One method for determining the LCM of 5760 and 5766 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 5760's prime factorization:

Prime factors of 5760 are 2, 3,5.

5760 = 2⁷×3²×5¹

And this is 5766's prime factorization:

Prime factors of 5766 are 2, 3,31.

5766 = 2¹×3¹×31²

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, 3,5,31

2⁷×3²×5¹×31² = 5535360

This shows that the LCM of 5760 and 5766 is 5535360.

The first step in determining the Least Common Multiple of 5760 and 5766 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 5760 and 5766:

Lets look at the first ten multiples of these numbers, 5760 and 5766:

5760,11520,17280,23040,28800,34560,40320,46080,51840,97920 are the first ten multiples of 5760.

5766,11532,17298,23064,28830,34596,40362,46128,51894,98022 are the first ten multiples of 5766.

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 5760 and 5766, for example, are 69120, 97920, and 92256. 5535360 is the least common multiple since it is the smallest.

5760 and 5766 have an LCM of 5535360.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5760 and 5766, than apply into the LCM equation.

GCF(5760,5766) = 6
LCM(5760,5766) = ( 5760 × 5766) / 6
LCM(5760,5766) = 33212160 / 6
LCM(5760,5766) = 5535360

1. What is the LCM of 5760 and 5766?

The LCM of 5760 and 5766 is 5535360.

2. How to find the lowest common multiple of 5760 and 5766?

To find the lowest common multiple of 5760 and 5766, we have to get the multip;es of both numbers and identify the least common multiple in them which is 5535360.

3. What are the Factors of 5760?

Answer: Factors of 5760 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 60, 64, 72, 80, 90, 96, 120, 128, 144, 160, 180, 192, 240, 288, 320, 360, 384, 480, 576, 640, 720, 960, 1152, 1440, 1920, 2880, 5760. There are 48 integers that are factors of 5760. The greatest factor of 5760 is 5760.

4. What are the Factors of 5766?

Answer: Factors of 5766 are 1, 2, 3, 6, 31, 62, 93, 186, 961, 1922, 2883, 5766. There are 12 integers that are factors of 5766. The greatest factor of 5766 is 5766.

Answer:

Least Common Multiple of 5760 and 5766 = 5535360

Step 1: Find the prime factorization of 5760

5760 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5

Step 2: Find the prime factorization of 5766

5766 = 2 x 3 x 31 x 31

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

LCM = 5535360 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 31 x 31

Step 4: Therefore, the least common multiple of 5760 and 5766 is 5535360.