# Highest common Factor

As the name suggests it is the common factor of numbers which is the highest.

Example – We need HCF for 12 and 18

Step -1 – Factors of 12
are 1, 2, 3, **6**
12

Step -2 – Factors of 18 are 1, 2, 3, **6**, 9, 18

The common factors are 1, 2 ,3, 6.

*Highest factor is 6. Hence the HCF is 6. *

Another example

Lets find the HCF for the numbers 20 , 28 ,36

20 – 1, 2, **4**, 5, 10, 20

28 – 1, 2, **4**, 7, 14, 28

36- 1, ,3, **4**, 6, 9, 18, 36

Here the common factors are 1, 2, 4 .

**The highest among these is 4. Hence the HCF for 20,28 & 36 is 4.**

## Least common multiple

Here too we need to check the common multiples of both numbers.

Example – lets find for 12 and 18

Multiples are of 12 are

(12×1=12 , 12×2=24 , 12×3=36 …….) 12 , 24 , 36, 48, 60 etc.

Multiples of 18 are

(18×1=18 , 18×2=36 , 18×3=54 …….) 18, 36 ,54, 72 ,90 etc.

If we see the common multiple is 36. Hence the LCM for 12 and 18 is 36.

Another way of finding out is by factoring starting with least prime no 2.

Here Multiply 2 X 3 X 2X 3 = 36 which is the LCM.