Question 27325: what number less than 3000 when divided by 10 has a remainder of 9 and when divided by 9 has a remainder of 8 and when divided by 8 has a remainder of 7 and when divided by 7 has a remiander of 6 and when divided by 6 has a remainder of 5 and when divided by 5 has a remainder of 4 when divided by 4 has a reaminder of 3 when divided by 3 has a remainder of 2 and when divided by 2 has a remainder of 1 and when divided by has a remainder of 0
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! what number less than 3000 when divided by 10 has a remainder of 9 and when divided by 9 has a remainder of 8 and when divided by 8 has a remainder of 7 and when divided by 7 has a remiander of 6 and when divided by 6 has a remainder of 5 and when divided by 5 has a remainder of 4 when divided by 4 has a reaminder of 3 when divided by 3 has a remainder of 2 and when divided by 2 has a remainder of 1 and when divided by has a remainder of 0
THAT IS ALL DIVISORS FROM 2 TO 10 RESULT IN LEAVING A REMAINDER OF ONE LESS THAN THE DIVISOR.
SO LEAST SUCH NUMBER CAN BE FIRST FOUND BY FINDING LCM OF THESE NUMBERS
2|2,3,4,5,6,7,8,9,10
........................
2|1,3,2,5,3,7,4,9,5
...........................
3|1,3,1,5,3,7,2,9,5
.............................
5|1,1,1,5,1,7,2,3,5
......................
.|1,1,1,1,1,7,2,3,1
..........................
LCM = 2*2*3*5*7*2*3=2520
SO THE NUMBER IS ONE ONE LESS THAN THIS ..THAT IS...2520-1=2519.
THE NEXT NUMBER HAS TO BE A MULTIPLE OF THE LCM LESS ONE THAT IS 2*2520-1....BUT THAT WILL BE OVER 3000...HENCE THE ANSWER IS 2519.
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