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

Hey. Out of all the given option only 364 is the multiple of 7. Question is solved there itself.

The question is a bit confusing but once you get it, it is ridiculously easy to solve. We are basically looking for a number X that has the following properties:
X/7 - no remained
x/6 - remainder of 4
X/9 - remainder of 4
X/15 - remainder of 4
X/18 - remainder of 4

Ideally, one would try and find the LCM of 6, 9, 15 and 18 but we already know the number involved is a multiple of 7 so we can quickly eliminate by dividing everything by 7. Turns out only one option remains. Check if they all divide by 6, 9, 15 and 18 to give a remainder of 4 and this is one of the easiest questions that can be asked.

How can you find the value of k=4 ? conclude please.

It can not be 1, 2, 3 because if we substitute these numbers the result which is not divisible by 7. Let's check out. The only least number is 4.

How can u choose the value of k=4 ? It can be 2 also know.

How k=4 comes?

Isn't it the least common multiple of 6, 7, 9, 15 and 18 with a remainder 4?

6+9+15+18 = 48.
48*7 = 336.

7*4 = 28.
Then 336+28 = 364.

364/48 = 7.5833.

Answer = 7.
Remainder = 4.

Is this right?

Is it for all cases we put the value of remainder in k; e.g if 7 is remainder then we should keep the value of k = 7? Is it general or anything else?

Correct answer is 94. Read question carefully.