# HCF and LCM of Fractions Calculation

Calculator that calculates the HCF and LCM of any number of given fractions separated by comma.

### Formula :

#### HCF = HCF of numerators / LCM of denominators

#### LCM = LCM of numerators / HCF of denominators

### HCF (Highest Common Factor) :

In mathematics, HCF is the short form of Highest Common Factor. It is also called the largest common factor. On finding factors of more than one number, some numbers are found to be common. The largest factor found in common factors is called HCF.### LCM (Least Common Multiple) :

In mathematics, LCM is the short form of the lowest common factor. It is also called the largest common factor. The least common multiple of more than one number is the smallest number among all common multiples of a given number.### Method to calculate HCF:

**HCF can be calculated using the given below methods :**

### Method 1. Factoring

Example: Find the HCF of 8 and 10 using factors:

Step 1: List all of the factors of the given numbers.

Factors of 10: 1, 2, 5, 10

Factors of 8 : 1, 2, 4, 8

Step 2: Numbers that exist in the factors of both numbers must be the greatest common number. In this case, 2 is the largest common number in both of them.

Hense, HCF (8, 10) = 2

### Method 2. Prime factorization

Example: Find the HCF of 20, 25, and 30 using prime factorization?

Step 1: List the prime factors of the given numbers.

Prime factors of 10: 2 × 5

Prime factors of 15: 3 × 5

Prime factors of 30: 2 × 3 × 5

Step 2: Mark the numbers that are common in the prime factors of all three numbers.

10: 2 × **5**

15: 3 × **5**

30: 2 × 3 × **5**

Hense HCF (10, 15, 30) = 5

When there are more than one common number then we have to multiply all common numbers to get the HCF.

### Methods to calculate LCM:

LCM can be calculated using given below methods:

### Method 1. Prime factorization method :

Example: Find LCM of 20, 30, and 50 using prime factorization?

Step 1: List the prime factors of the given numbers.

20 : 2 x 2 x 5

30 : 2 x 3 x 5

50 : 2 x 5 x 5

Step 2: To get the LCM we have to then multiply the prime factors.

Hense, LCM (20, 30, 50) = 300

### Method 2. List of multiples

Example: Find the LCM of 5 and 15 with the listing multiples method?

Step 1: Write down the multiples of the given numbers.

Multiples of 5 = 5 ,10, 15, 20, 25, 30, 35

Multiples of 15 = 15, 30, 45, 60, 75, 90, 105…

Step 2: Highlight the common multiple in the multiples of given numbers.

5 = 5 ,10, 15, 20, 25, 30, 35

15 = 15, 30, 45, 60, 75, 90, 105…

So, LCM (10, 15) = 15