LCM Using Prime Factorization

The expanded form of LCM is Lease common multiple which means find the common multiple with least value for a given set of numbers. This can be done by using either prime numbers or by using composite numbers or with a combination of prime numbers and composite numbers. The LCM can also be written with exponents.
Steps to Find the Lcm Using Prime Factorization:

Step 1: Write the given set of numbers.

Step 2: Take the first number from the given set.

Step 3: Write the number with the multiples of prime numbers.

Step 4: Repeat step 2 and Step 3 for all the numbers in a given set.

Step 5: Choose the highest exponent term form all and multiply it to get LCM of given numbers.
Example Problems – Lcm Using Prime Factorization:

Example 1- LCM using prime factorization:

Find the LCM of 30 and 10.

Solution:

The given numbers are 30 and 10.

First it needs to find the prime factors of 30.

30 = 2*15

     = 2 * 3  * 5

The prime factors of 30 are 21, 31 and 51.

Next it needs to find the prime factors of 10.

10 = 2 * 5.

The prime factors of 10 are 21 and 51.

The highest exponent of all terms is 21, 31 and 51.

The LCM of 30 and 10 is 2 * 3* 5 `=>` 30.

My forthcoming post is on prime factorization algorithm, adding and subtracting rational expressions with unlike denominators will give you more understanding about Algebra

Example 2- LCM using prime factorization:

Find the LCM of 42 and 60.

Solution:

The given numbers are 42 and 60.

First it needs to find the prime factors of 42.

42 = 2*21

     = 2 * 3  * 7

The prime factors of 30 are 21, 31 and 71.

Next it needs to find the prime factors of 60.

60 = 2 * 30

     = 2 * 2 * 15

     = 2* 2 * 3* 5

The prime factors of 10 is 22 , 31 and 51.

The highest exponent of all terms is 22, 31, 51 and 71.

The LCM of 30 and 10 is 22 * 3* 5* 7 `=>` 420.

Example 3- LCM using prime factorization:

Find the LCM of 50 and 100.

Solution:

The given numbers are 50 and 100.

First it needs to find the prime factors of 50.

50 = 2*25

     = 2 * 5  * 5

The prime factors of 50 are 21 and 52

Next it needs to find the prime factors of 60.

100 = 2 * 50

       = 2 * 2 * 25

       = 2* 2 * 5* 5

The prime factors of 10 is 22 and 52

The highest exponent of all terms is 22 and 52

The LCM of 30 and 10 is 22 * 52 `=>` 100

Equivalent Percentage

Percentage is a number represents fraction of 100. In percentage, numerator is any number but denominator is only 100. So that it is called as Percentage. We can denote percentage of a number by using symbol %.

Example of Percentage: `50/100` (or) 50%

Equivalent percentage is a percentage for equivalent fraction or decimal.

In this article, we shall see about how to find equivalent percentage for given values.
Example Problems – Equivalent Percentage:

Problem 1:

What is the equivalent percentage of 5 out of 10.

Solution:

Step 1:

First, we divide numerator by denominator.

So `5/10` = 0.5

Step 2:

Multiply and divide the above decimal value by 100.

 `(0.5*100)/100`

Step 3:

So we get, `50/100` is equal to 50%.

Answer:

Equivalent percentage of `5/6` is 50%.

Problem 2:

What is the equivalent percentage of 6 out of 8.

Solution:

Step 1:

First, we divide numerator by denominator.

So `6/8` = 0.75

Step 2:

Multiply and divide the above decimal value by 100.

 `(0.75*100)/100`

Step 3:

So we get, `75/100` is equal to 75%.

Answer:

Equivalent percentage of `6/8` is 75%.

Problem 3:

What is the equivalent percentage of fraction `4/5` .

Solution:

Step 1:

First, we divide numerator by denominator.

So `4/5` = 0.8

Step 2:


Multiply and divide the above decimal value by 100.

`(0.8*100)/100 `

Step 3:

So we get, `80/100` is equal to 80%.

Answer:

Equivalent percentage of `4/5` is 80%.

Problem 4:

What is the equivalent percentage of 0.06?

Solution:

Multiply and divide the given decimal value by 100

`(0.06*100)/100 `

So we get, `6/100` is equal to 6%.

Answer:

Equivalent percentage of 0.06 is 6%.

Problem 5:

What is the equivalent percentage of 0.25?

Solution:

Multiply and divide the given decimal value by 100

`(0.25*100)/100 `

So we get, `25/100` is equal to 25%.

Answer:

Equivalent percentage of 0.25 is 25%.
Practice Problems: Equivalent Percentage

Problem 1:

What is the equivalent percentage of `8/5` ?

Answer:

160%

 Problem 2:

What is the equivalent percentage of `10/1000` ?

Answer:

1%

Problem 3:

What is the equivalent percentage of 0.81?

Answer:

81%

Problem 4:

What is the equivalent percentage of 0.025?

Answer:

2.5%