Given Numbers are 10, 18

We can find the LCM of 10, 18 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 10 and 18

Multiples of 10 =10,20,30,40,50,60,70,80,90,100,110,120,130,140,150,160,170,

Multiples of 18 =18,36,54,72,90,108,126,144,162,180,198,216,234,252,270,288,306,

Now, get the least common multiple of 10, 18 which is 90

So, the LCM of 10, 18 is 90.

One method for determining the LCM of 10 and 18 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 10's prime factorization:

Prime factors of 10 are 2,5.

10 = 2¹×5¹

And this is 18's prime factorization:

Prime factors of 18 are 2,3.

18 = 2¹×3²

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: 2,5,3

2¹×3²×5¹ = 90

This shows that the LCM of 10 and 18 is 90.

The first step in determining the Least Common Multiple of 10 and 18 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 10 and 18:

Lets look at the first ten multiples of these numbers, 10 and 18:

10,20,30,40,50,60,70,80,90,170 are the first ten multiples of 10.

18,36,54,72,90,108,126,144,162,306 are the first ten multiples of 18.

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 10 and 18, for example, are 120, 170, and 288. 90 is the least common multiple since it is the smallest.

10 and 18 have an LCM of 90.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10 and 18, than apply into the LCM equation.

GCF(10,18) = 2
LCM(10,18) = ( 10 × 18) / 2
LCM(10,18) = 180 / 2
LCM(10,18) = 90

1. What is the LCM of 10 and 18?

The LCM of 10 and 18 is 90.

2. How to find the lowest common multiple of 10 and 18?

To find the lowest common multiple of 10 and 18, we have to get the multip;es of both numbers and identify the least common multiple in them which is 90.

3. What are the Factors of 10?

Answer: Factors of 10 are 1, 2, 5, 10. There are 4 integers that are factors of 10. The greatest factor of 10 is 10.

4. What are the Factors of 18?

Answer: Factors of 18 are 1, 2, 3, 6, 9, 18. There are 6 integers that are factors of 18. The greatest factor of 18 is 18.

Answer:

Least Common Multiple of 10 and 18 = 90

Step 1: Find the prime factorization of 10

10 = 2 x 5

Step 2: Find the prime factorization of 18

18 = 2 x 3 x 3

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

LCM = 90 = 2 x 3 x 3 x 5

Step 4: Therefore, the least common multiple of 10 and 18 is 90.