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

@All.

Hai I have a doubt, everyone is explaining from 840k+3 but here the doubt is we got lcm 840 if 5 6 7 8 divide the 840 answer is 0.

So, 840 + 3=843 now we will get remainder 3 but here 5 is divisor 840 is dividend so how you come 840k+3? Explain it.

Simply we can solve this by;

1+6+8+3=18
1+6+7+7=21
Same as other;

18 is divided by 9 and then B is correct.

What is the Value of k?

@Aall.

The solution is;
Check :A-1677 divisible given no 5 we get reminder 2 so this not correct.

Then next B-1683 divisible given no 5 we will get reminder 3 next.
Divisible no 6 we get reminder 3.
Divisible 7 and 8 also we get reminder 3.
Then; 1+6+8+3=18, divisible by 9 so answer is B correct.

In simple when we go with options

Option A)1677
1677/9, remainder=3.

Option B) 1683
1683/9, remainder=0.

Option C) 2523
2523/9, remainder=3.

Option D) 3363
3363/9, remainder=3.

When 1683/5, 1683/6, 1683/7, 1683/8 leaves the remainder of 3 and 1683/9 leaves no remainder.

Hence, the correct option is B.

How k= 2? Explain.

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.

Thanks for the answer @Suchita.

Well said, thanks @Suchita.

Apply the divisibility test of 9 to the options, in this case only 1683 and 3363 are divisible by 9. Since they have asked for the least number 1683 is the answer.