Given Numbers are 28, 35

We can find the LCM of 28, 35 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 28 and 35

Multiples of 28 =28,56,84,112,140,168,196,224,252,280,308,336,364,392,420,448,476,

Multiples of 35 =35,70,105,140,175,210,245,280,315,350,385,420,455,490,525,560,595,

Now, get the least common multiple of 28, 35 which is 140

So, the LCM of 28, 35 is 140.

One method for determining the LCM of 28 and 35 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 28's prime factorization:

Prime factors of 28 are 2,7.

28 = 2²×7¹

And this is 35's prime factorization:

Prime factors of 35 are 5,7.

35 = 5¹×7¹

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: 2,7,5

2²×5¹×7¹ = 140

This shows that the LCM of 28 and 35 is 140.

The first step in determining the Least Common Multiple of 28 and 35 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 28 and 35:

Lets look at the first ten multiples of these numbers, 28 and 35:

28,56,84,112,140,168,196,224,252,476 are the first ten multiples of 28.

35,70,105,140,175,210,245,280,315,595 are the first ten multiples of 35.

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 28 and 35, for example, are 336, 476, and 560. 140 is the least common multiple since it is the smallest.

28 and 35 have an LCM of 140.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 28 and 35, than apply into the LCM equation.

GCF(28,35) = 7
LCM(28,35) = ( 28 × 35) / 7
LCM(28,35) = 980 / 7
LCM(28,35) = 140

1. What is the LCM of 28 and 35?

The LCM of 28 and 35 is 140.

2. How to find the lowest common multiple of 28 and 35?

To find the lowest common multiple of 28 and 35, we have to get the multip;es of both numbers and identify the least common multiple in them which is 140.

3. What are the Factors of 28?

Answer: Factors of 28 are 1, 2, 4, 7, 14, 28. There are 6 integers that are factors of 28. The greatest factor of 28 is 28.

4. What are the Factors of 35?

Answer: Factors of 35 are 1, 5, 7, 35. There are 4 integers that are factors of 35. The greatest factor of 35 is 35.

Answer:

Least Common Multiple of 28 and 35 = 140

Step 1: Find the prime factorization of 28

28 = 2 x 2 x 7

Step 2: Find the prime factorization of 35

35 = 5 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 = 140 = 2 x 2 x 5 x 7

Step 4: Therefore, the least common multiple of 28 and 35 is 140.