Aptitude - Problems on H.C.F and L.C.M - Discussion

hai vishnu...why should divide with only 40 why cant we do that with reaming no given there?

@vishnu.

Their is no need to divide by 40.

Wow should we divide 9999 by 600

i) 1st we find the greatest 4 digit number

ii) Then find the lcm of 15,25,40 ,75 ,is 600 ,so 600 is least number by which 15,25,40,75.so all the multiple of 600 is divisible by 15,25,40,75

iii) Then find multiple of 600 which is less than 999

iv) So we divide 9999 by 600

and get 399 as remainder,

If substract 399 from 9999 tnen we get that number

9999 - 3999 = 9600

Why to subtract remainder from 9999 ?

We have to find greatest 4 digit number so it may be between 9000 to 9999 let the number be x

this x should be divisible by 15, 25, 40 and 75 so take common least nnumber from all factors i.e l.c.m=600

therefore x is also divisible by 600 that means when x is divided by 600 remainder should be '0' but how can we find that number??

that number x lies between 9000 to 9999

take any number between them i.e take 9000,..9010,...9090...9900...9997,9998,9999 as your wish

so insted of 9999 here iam taking 9998 which is divided by 600

so remainder is 398 so substract 398 from 9998 i.e 9998-398=9600

why we wre substracting is because x should be divisible 600 and
remaider should be '0' so x is 9600 thats it

Good answer rahul.

Find the LCM of 15, 25, 40 and 75 which is 600.

Now, find out the multiples of 600 i.e.
600*1=600
600*2=1200
600*3=1800
........
600*16=9600
600*17=10200

We can see that the greatest number of four digits is 9600 and hence 9600 is the answer.

Greatest number of 4-digits is 9999.

L.C.M. of 15, 25, 40 and 75 is 600.
(I understood till above, but how come 9999 divided by 600 is 399??)

On dividing 9999 by 600, the remainder is 399??

Required number (9999 - 399) = 9600??

Find LCM AND HCF OF
x3+2x2-4x-8 and2x3+7x2+4x-4

There can be another approach. Just find the L.C.M. of the nos. The L.C.M. comes to be 600. Now check which is the greatest no. which is getting divided by 600.

Numbers of option B and option D are not getting divided by 600 and between option B and C (which are getting divided by 600) the number of option C is the greatest no. divisible by 600

In this way I guess it would be quicker than dividing 9999 and then subtracting the remainder.