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

Basic rule : a/b gives q as remainder..(not exactly divisible)

then a-q/b ...no remainder.....(exactly divisible)
also
a/b+q -------no remainder .....(exactly divisible)


See the number say x is exactly divisible by the given nos: 12 , 16 , 18 , 21, 28..when 7 is substracted form x..ok

LCM 1008 is a single no that represents 12 16 18 21 and 28.

the no x is exactly divisible by 1008 (so obviously x is greater than 1008)only when 7 is substracted from it..

which means x/1008 will give 7 as remainder...

so adding 7 to 1008 gives 0 as remainder..

ie...x / 1008 + 7 ......0 remainder

also we can write

x-7 / 1008 ..0 remainder....

Hope it is clear..Thank You..

Easy and short method:

As given in question when 7 is subtracted from a number, the number is divisible by 12,16,18, and so on;

So with the help of the given option;

1008 - 7 =1001 which is not divisible by 12 (use 12 because as given in question, the number is divisible by 12,16,18)

1015 -7 = 1008 which is divisible by 12.

So the answer is 1015.

So,

Let assume that the smallest number is X. And it diminished by 7 so it will be like
= X-7.

Now, this number is divisible by 12, 16, 18, 21, 28 and also it is divisible by LCM OF them.
So the LCM = 1008.
So now,
X-7/1008 = 1.
X = 1015.

Hope it helps.

Guys the it has been asked to find the number when when subtracted will be divisible by given numbers.

Just take one by one and subtract 7.

1015-7 = 1008 which is exactly divisible by given numbers.

As here 1015 is diminished by 7. Its not adding 1008+1015.

Simple it has to give any number is diminished by 7.

Let the no be 'x' if it diminishes (subtract) 7.

It is equal to the lcm of the 12, 16, 18, 21and 28.

So, x - 7 = (lcm of 12, 16, 18, 21, 28).

x - 7 = 1008.
x = 1008 + 7.
x = 1015 this is the answer.

Question says, that no (say x) which when subtracted by 7 gives you an exactly divisible no by 12, 16, 18, 21, 28.

Here the exactly divisible no is 1008.

And the number from which you get 1008 after subtracting 7 is 1015 which was asked to find out.

Take one by one option to get the answer in the following method :

1008 - 7 = 1001/1008(L.C.M. of 12,16, 18, 21, 28) here reminder is not coming 0.

1015 - 7 = 1008/1008 here reminder is coming 0.

So option B is correct answer.

No need to do mathematics. Option B is the only odd number among all. So when 7 is subtracted from other even numbers, the answer will be odd and can't be divisible by 12, 16, 18 and 28.

Let the smallest number be x then x-7 should be divisible by 12, 16, 18, 21, 28. Then substitute the values of the options given in the answer in x to find the smallest number.

Ya, LCM of the numbers is 1008 which is equal to the smallest no diminished by 7,
So 1008 = x-7,

Then smallest no, x=1008+7.
That's why we are added with 7.