Find the greatest number of 5 digits exactly divisible by 12,15 & 36.

Asked by Kalita Padmanath | 13th Jul, 2015, 12:54: PM

Expert Answer:

W e space n e e d space t o space f i n d space t h e space g r e a t e s t space n u m b e r space o f space 5 space d i g i t s space e x a c t l y space d i v i s i b l e space b y space 12 comma space 15 space a n d space 36. L e t space u s space f i r s t space f i n d space t h e space L C M space o f space 12 comma space 15 space a n d space 36 12 equals 2 squared cross times 3 15 equals 3 cross times 5 36 equals 2 squared cross times 3 squared T h u s comma space L C M space o f space 12 comma space 15 space a n d space 36 equals 2 squared cross times 3 squared cross times 5 equals 180 G r e a t e s t space f i v e space d i g i t space n u m b e r equals 99999 W e space c a n space f i n d space t h e space r e m a i n d e r space w h e n space 99999 space i s space d i v i d e d space b y space 180 space b y space E u c l i d apostrophe s space l e m m a. T h u s comma 99999 equals 555 cross times 180 plus 99 T h e r e f o r e comma space 99 space i s space t h e space r e m a i n d e r space w h e n space 99999 space i s space d i v i d e d space b y space 180. S u b t r a c t space t h e space r e m a i n d e r space 99 space f r o m space 99999. S o comma space G r e a t e s t space f i v e space d i g i t space n u m b e r space w h i c h space i s space e x a c t l y space d i v i s i b l e space b y space 12 comma space 15 space a n d space 36 equals 99999 minus 99 equals 99900

Answered by Vimala Ramamurthy | 14th Jul, 2015, 10:55: AM