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

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"Loneliness is the most terrible poverty."
- Mother Teresa
19.

The smallest number which when diminished by 7, is divisible 12, 16, 18, 21 and 28 is:

 [A]. 1008 [B]. 1015 [C]. 1022 [D]. 1032

Explanation:

Required number = (L.C.M. of 12,16, 18, 21, 28) + 7

= 1008 + 7

= 1015

 Syed said: (Tue, Aug 23, 2011 06:13:28 AM) Can anyone tell why adding 7 with 1008

 Dipak said: (Sun, Aug 28, 2011 12:59:59 AM) Diminish means subtract than why adding 7?

 Chinna said: (Fri, Oct 28, 2011 11:34:36 AM) Diminish means subtract. Why adding 7 ? Can anyone explain please ?

 Abhishek Yadav said: (Fri, Nov 4, 2011 11:01:10 AM) 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.

 Vani Varma said: (Wed, Feb 8, 2012 02:14:36 PM) 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..

 Merry said: (Tue, Aug 28, 2012 12:10:33 PM) Please tell me details explain, I don't understand why you adding 7.