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

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.

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.

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

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..

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.

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

Diminish means subtract than why adding 7?

Can anyone tell why adding 7 with 1008