Given Numbers are 269, 274

We can find the LCM of 269, 274 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 269 and 274

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

Multiples of 274 =274,548,822,1096,1370,1644,1918,2192,2466,2740,3014,3288,3562,3836,4110,4384,4658,

Now, get the least common multiple of 269, 274 which is 73706

So, the LCM of 269, 274 is 73706.

One method for determining the LCM of 269 and 274 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 269's prime factorization:

Prime factors of 269 are 269.

269 = 269¹

And this is 274's prime factorization:

Prime factors of 274 are 2,137.

274 = 2¹×137¹

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:269, 2,137

2¹×137¹×269¹ = 73706

This shows that the LCM of 269 and 274 is 73706.

The first step in determining the Least Common Multiple of 269 and 274 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 269 and 274:

Lets look at the first ten multiples of these numbers, 269 and 274:

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

274,548,822,1096,1370,1644,1918,2192,2466,4658 are the first ten multiples of 274.

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 269 and 274, for example, are 3228, 4573, and 4384. 73706 is the least common multiple since it is the smallest.

269 and 274 have an LCM of 73706.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 269 and 274, than apply into the LCM equation.

GCF(269,274) = 1
LCM(269,274) = ( 269 × 274) / 1
LCM(269,274) = 73706 / 1
LCM(269,274) = 73706

1. What is the LCM of 269 and 274?

The LCM of 269 and 274 is 73706.

2. How to find the lowest common multiple of 269 and 274?

To find the lowest common multiple of 269 and 274, we have to get the multip;es of both numbers and identify the least common multiple in them which is 73706.

3. 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.

4. What are the Factors of 274?

Answer: Factors of 274 are 1, 2, 137, 274. There are 4 integers that are factors of 274. The greatest factor of 274 is 274.

Answer:

Least Common Multiple of 269 and 274 = 73706

Step 1: Find the prime factorization of 269

269 = 269

Step 2: Find the prime factorization of 274

274 = 2 x 137

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

LCM = 73706 = 2 x 137 x 269

Step 4: Therefore, the least common multiple of 269 and 274 is 73706.