Important shortcut tricks on lcm and hcf

Important shortcut formula on hcf and lcm:

1. Hcf of numbers*Lcm of numbers=Product of numbers

2. To find the greatest number that will divide x,y and z :
Hcf of x,y,z.

3. The greatest number that will divide x,y,z leaving same remainders in each case will be hcf of |(x-y)|,|(y-z)|,|(z-x)|

Shortcut formule on number system

Important shortcut formula on number system :

1.  To find the larger between ³√3 and ⁴√5

Solution: 
 Take lcm of surds which are 3 and 4 here .
Lcm of 3 and 4 is 12 
Convert each surd into surd of 12.
³√3=¹²√3⁴=¹²√81
⁴√5=¹²√5³=¹²√125

Clearly ¹²√125 >¹²√81 
So ⁴√5 is greater.

work and time shortcut formula

work  formula

A can do a work in x days
then A's work rate( work done per day)= 1/x

B do a work in y days then
B's work rate=1/y


1.  A+B work per day= 1/x+1/y =(x+y)/xy
     A+B  will finish work in = xy/(x+y) days

Average of number series

Average and sum of natural numbers series

1 .Sum of all first n natural numbers is equal to

Sum=n(n+1)/2

and we know that 

Average= sum/number

so average of first n natural numbers is 

Average=n(n+1)/2n=(n+1)/2

Shortcut formula for countinous percentage change..

  Some important formula on percentage.

let x is original/initial term , y is final term and p,q,r are the continuous percentage changes 

Or you can say

x changes in y after getting p%,q%,r% changes which can be increment or decrement.


In increment case :

1. Final value, y=x((100+p)(100+q)(100+r))/100*100*100

Average shortcut formula

Average shortcut formula for solving avearge questions:




This can be modified in other formula like :

Number(change in average)=  Added- Removed