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How do you find the least number when divided by 16 and 18 gives remainders 2 and 12?
Wiki User
∙ 12y ago
Suppose the number is n
Then n = 16x + 2 for some non-negative integer x
and n = 18y + 12 for some non-negative integer y.
That gives 16x + 2 = 18y + 12
which can be simplified to 8x = 9y + 5
or x = (9y + 5)/8
Since x is an integer, 8 must go into 9y+5 evenly.
That requires that 9y leaves a remainder of 3 when divided by 8.
Since 9 and 8 are coprime, y = 3
So n = 18*3 + 12 54+12 = 66
Wiki User
∙ 12y ago
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