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

Please anyone explain how will come lcm 600 from the 4 digits.

I didn't understand. Please help me.

Lcm =600,
Then 600*14= 8400,
But I need a range between 9000 to10000,
Then 600*15=9000,
But 600*16= 9600,
600*17=10200 but I want the biggest number below 10000
So 9600 is the right answer.

Sure the greatest 4 digit no. is 9999.
Here we have to find the greatest 4 digit number divisible by 15,25,40 and 75( that is the number divisible by 600 as the LCM of 15,25,40 and 75 is 600).it means the greatest 4 digit number divisible by 600 is only the greatest number divisible by 15,25,40 and 75.

To find 4 digit greatest number here we must find the nearest 4 digit number less 9999 that is possible by dividing the 9999 by the LCM and subtracting LCM.

=> 9999÷600
=> 9999-(600*16)
=>9999-(9600)
=>399 is remainder.

We can calculate the required number by subtracting 399= 9999-399 or,
we can directly find the nearest number divisible by 600= 600*16=9600.

Let consider 15 which is div by 3. Check 9000, 9400, 9600, 9 800 is divisible or not.

We know 9400 and 9800 are not divisible. Hence we omitting that two.

Again look for 9000 and 9600. We have 15, 25, 40, 75 by simply seeing these numbers all are not divided num 9000. Hence our answer is 9600.

Highest four digit possible number is 9999 because 10000 is a 5 digit number.

Why 9999? Explain.

The greatest number given there is first to come.
9800 which is not divisible by 600.
9600 which is divisible,
So answer is 9600.

Why we take LCM of these Numbers?

Why Not HCF? Can Anyone explain?

Here it is 600*4^2=9600.

How do you get 399 on dividing 9999 by 600 please explain?