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

Can anyone tell why adding 7 with 1008

Diminish means subtract than why adding 7?

Diminish means subtract. Why adding 7 ? Can anyone explain please ?

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.

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..

Please tell me details explain, I don't understand why you adding 7.

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 no be X,
Lcm of 12,16,18,21,28 = 1008.

Here in question, they have,
Diminished by 7, so, x-7 = 1008.

x = 1008+7 = 1015.

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.