Lowest Number
If you divide a particular number by 4, there's a remainder of 1; if you divide the same number by 5, there's a remiander of 2; and if you divide it by 6, there's a remainder of 3. There's probably lots of numbers which would meet the stated criteria.
What is the lowest number which complies with problem statement?
What is the lowest number which complies with problem statement?
posted by Zaux at
12:36 PM
12 Comments:
the number is 57
the number is 57
57
I found 16 less than 1000
1 57
2 117
3 177
4 237
5 297
6 357
7 417
8 477
9 537
10 597
11 657
12 717
13 777
14 837
15 897
16 957
Did you note something common about these?
57 + 60 = 117
117 + 60 = 177
and so on... difference of 60
57 is obviously correct
All numbers that are 3 less that a multiple of 60 fit the bill; i.e., 60k-3 where k is any integer.
(60k-3) = -3 mod 4 = 1
(60k-3) = -3 mod 5 = 2
(60k-3) = -3 mod 6 = 3
60 is the least common multiple of 4, 5, and 6.
This post has been removed by the author.
This post has been removed by the author.
This post has been removed by the author.
Too tired again. Silly errors fixed.
I've never really come to grips with how to do this type of math. Fortunately in this case, I can see a simple way to do it.
We have x = 1 (mod 4), x = 2 (mod 5) and x = 3 (mod 6)
Now for the lucky bit: x+3 = 0 (mod 4,5 and 6).
LCM(4,5,6) = 60 and so x+3 = 0 (mod 60)
Hence x+3 = 60 => x = 57
is the smallest number that does it.
http://www.wolframalpha.com/input/?i=LCM%5B3%2C4%2C5%5D
... and for completenes, obviously can add arbitrary multiples of 60 to 57.
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