Given Numbers are 5760, 5767

We can find the LCM of 5760, 5767 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 5760 and 5767

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

Multiples of 5767 =5767,11534,17301,23068,28835,34602,40369,46136,51903,57670,63437,69204,74971,80738,86505,92272,98039,

Now, get the least common multiple of 5760, 5767 which is 33217920

So, the LCM of 5760, 5767 is 33217920.

One method for determining the LCM of 5760 and 5767 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 5767's prime factorization:

Prime factors of 5767 are 73,79.

5767 = 73¹×79¹

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, 73,79

2⁷×3²×5¹×73¹×79¹ = 33217920

This shows that the LCM of 5760 and 5767 is 33217920.

The first step in determining the Least Common Multiple of 5760 and 5767 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 5760 and 5767:

Lets look at the first ten multiples of these numbers, 5760 and 5767:

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

5767,11534,17301,23068,28835,34602,40369,46136,51903,98039 are the first ten multiples of 5767.

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 5767, for example, are 69120, 97920, and 92272. 33217920 is the least common multiple since it is the smallest.

5760 and 5767 have an LCM of 33217920.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5760 and 5767, than apply into the LCM equation.

GCF(5760,5767) = 1
LCM(5760,5767) = ( 5760 × 5767) / 1
LCM(5760,5767) = 33217920 / 1
LCM(5760,5767) = 33217920

1. What is the LCM of 5760 and 5767?

The LCM of 5760 and 5767 is 33217920.

2. How to find the lowest common multiple of 5760 and 5767?

To find the lowest common multiple of 5760 and 5767, we have to get the multip;es of both numbers and identify the least common multiple in them which is 33217920.

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 5767?

Answer: Factors of 5767 are 1, 73, 79, 5767. There are 4 integers that are factors of 5767. The greatest factor of 5767 is 5767.

Answer:

Least Common Multiple of 5760 and 5767 = 33217920

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 5767

5767 = 73 x 79

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

LCM = 33217920 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 73 x 79

Step 4: Therefore, the least common multiple of 5760 and 5767 is 33217920.