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

2 has come because 5*6*7*8 is 1683.

Thanks for the explanation @Suchita.

Good explanation, Thanks @Suchita.

Another shortcut which will work in this case is checking thew divisibility by 9.
only 1683 is divisible by 9 hence the answer is 1683. In case there is more numbers divisible by you have to check it as my previous answer.

You will not get this much time in solving the question in competitive exams. There is a shortcut in solving this.

First check divisibility of each number-3 with 5,6,7 and 8 and the divisibility of the number with 9.

a) 1677 -3=1674, it will not be divisible by 5 so no need to check with any other.
b)1683-3= 1680, Last digit is 0 hence divisible by 5. Divisible by 2 (even number) and 3 (sum = 15 is divisible by 3) hence divisible by 6.

Checking divisibility by 7-> 16-8*2= 0. hence divisible by 7.
It is divisible by 8 -> (8*21=168).
Sum of original number 1683 = 18 which is divisible by 9 hence 1683 is divisible by 9.
There is no other number smaller than 1683 Hence the answer is 1683.

Answer is just simple divide all option values by 9 which is exactly divisible is your answer. Just simple.

Lcm of 5,6,7, and8=840.
840÷9=93,leaves remainder =3.
multiply all the values=5*6*7*8=1680.
and leaves remainder are added =1680+3=1683.

Thanks @Suchita.

Super shorcut method. Thank you so much @Suchita.

How did you get that the req number is of the form 840k+ 3?