Mathematics on LCM

 problem is  what is the least number which when doubled will be exactly divisible by

12,18, 21 and 30



LCM  is  lowest common multiplier  

in LOWEST  is the minimum number which can be divided  not only by  12 but also 18, 21, and 30,

COMMON  means the number is common multiplier of 12, 18, 21,and 30 .

So if any set of numbers there is a common number can be achieved , which is divisible by every number of the set.

In this case the set of  numbers are  12,18,21, 30

Let us find this numbers LCM

3 || 12,18,21,30 |4
       2 || 4, 6, 7, 10
              2, 3, 7,  5

So LCM is   3x2x2x3x7x5 =  1260

1260 is lowest number which is divisible by 12.18. 21. 30

Now problem is asking  the lowest no which is doubled  Here doubled means twice or multiplied by two.

 Actual no is  1260 divided by 2 which is  630 is the required answer.

Problem 2
Now another problem is given like that

We have to find out the number which when diminished by 7 is exactly divisible by 12,16,18,21, and 28

Now we know that for each set or bunch of such nos there is a lowest number can be found out which is divisible by that numbers


So Lowest common multiplier (LCM) is the lowest no which we have to found out


12,16,18,21,28

on doing LCM  it is coming 1008

But the problem has still some twist

It is asking find a lowest number which is diminished (lowered) by 7

If 1008 is the lowest number the required number being asked to find out is 1008 +7= 1015