Given Numbers are 264, 269

We can find the LCM of 264, 269 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 264 and 269

Multiples of 264 =264,528,792,1056,1320,1584,1848,2112,2376,2640,2904,3168,3432,3696,3960,4224,4488,

Multiples of 269 =269,538,807,1076,1345,1614,1883,2152,2421,2690,2959,3228,3497,3766,4035,4304,4573,

Now, get the least common multiple of 264, 269 which is 71016

So, the LCM of 264, 269 is 71016.

One method for determining the LCM of 264 and 269 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 264's prime factorization:

Prime factors of 264 are 2, 3,11.

264 = 2³×3¹×11¹

And this is 269's prime factorization:

Prime factors of 269 are 269.

269 = 269¹

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, 3,11,269

2³×3¹×11¹×269¹ = 71016

This shows that the LCM of 264 and 269 is 71016.

The first step in determining the Least Common Multiple of 264 and 269 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 264 and 269:

Lets look at the first ten multiples of these numbers, 264 and 269:

264,528,792,1056,1320,1584,1848,2112,2376,4488 are the first ten multiples of 264.

269,538,807,1076,1345,1614,1883,2152,2421,4573 are the first ten multiples of 269.

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 264 and 269, for example, are 3168, 4488, and 4304. 71016 is the least common multiple since it is the smallest.

264 and 269 have an LCM of 71016.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 264 and 269, than apply into the LCM equation.

GCF(264,269) = 1
LCM(264,269) = ( 264 × 269) / 1
LCM(264,269) = 71016 / 1
LCM(264,269) = 71016

1. What is the LCM of 264 and 269?

The LCM of 264 and 269 is 71016.

2. How to find the lowest common multiple of 264 and 269?

To find the lowest common multiple of 264 and 269, we have to get the multip;es of both numbers and identify the least common multiple in them which is 71016.

3. What are the Factors of 264?

Answer: Factors of 264 are 1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 132, 264. There are 16 integers that are factors of 264. The greatest factor of 264 is 264.

4. What are the Factors of 269?

Answer: Factors of 269 are 1, 269. There are 2 integers that are factors of 269. The greatest factor of 269 is 269.

Answer:

Least Common Multiple of 264 and 269 = 71016

Step 1: Find the prime factorization of 264

264 = 2 x 2 x 2 x 3 x 11

Step 2: Find the prime factorization of 269

269 = 269

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

LCM = 71016 = 2 x 2 x 2 x 3 x 11 x 269

Step 4: Therefore, the least common multiple of 264 and 269 is 71016.