A number theory problem by MD Shad Ejaz Alam
Number Theory
Level
pending
Find the smallest positive integer,when divided by 2,3,4,5 and 6 leaves the remainder 1,2,3,4 and 5 respectively
The answer is 59.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
lets take the LCM of 2,3,4,5 and 6 is 60 the difference between the number and remainder in each case is [(2-1=1)],[(3-2=1)],[(4-3=1)],[(5-4=1)],[(6-5=1)] is 1. so,all the integers of the given set will be 60n-1 if n=1 then 60n-1=59 n=2 then 60n-1=119 so the smallest integer required is 59