I have got some chocolates to be distributed. when they are put in packets of 2,3,4 or 5 each, I am left with one. If they are put in packets of seven, I am left with none. What is the minimum nimber of chocolates that I have?

Asked by ca_vipin | 10th Oct, 2010, 12:50: PM

Expert Answer:

L e t space x space b e space t h e space n u m b e r space o f space c h o c l a t e s. space G i v e n space t h a t space w h e n space space c h o c l a t e s space a r e space p u t space i n space p a c k e t s space o f space 2 comma 3 comma 4 comma space o r space 5 space o n e space i s space l e f t. T h u s comma space w e space n e e d space t o space f i n d space t h e space L C M space o f space 2 comma 3 comma 4 comma 5 space a n d space a d d space o n e space t o space i t. A l s o space i f space t h e space c h o c l a t e s space a r e space space p u t space i n space p a c k e t s space o f space 7 space y o u space w i l l space l e f t space w i t h space n o n e. T h u s comma space i t space s h o u l d space b e space m u l t i p l e space o f space 7 space a f t e r space a d d i n g space o n e space t o space t h e space m u l t i p l e space o f space L C M space o f space 2 comma 3 comma 4 space o r space 5. T h u s comma space t h e space n u m b e r space o f space c h o c o l a t e s equals M i n i m u m space m u l t i p l e space o f space 7 open parentheses m u l t i p l e space o f space L C M space o f space 2 comma 3 comma 4 space o r space 5 space plus 1 close parentheses space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals M i n i m u m space m u l t i p l e space o f space 7 open parentheses m u l t i p l e space o f space 60 plus 1 close parentheses space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals M i n i m u m space m u l t i p l e space o f space 7 open parentheses 60 comma 120 comma 180 comma 240 comma 300 comma... plus 1 close parentheses space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals M i n i m u m space m u l t i p l e space o f space 7 open parentheses 61 comma 121 comma 181 comma 241 comma 301 comma.... close parentheses space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals M i n i m u m space m u l t i p l e space o f space 7 open parentheses 301 comma 721 comma.... close parentheses space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 301  space space space space

Answered by  | 7th Apr, 2015, 11:52: AM

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