SOLUTION: The least number when divided by 0.06, 0.008 and 0.16 gives integers as quotient is-

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Question 822570: The least number when divided by 0.06, 0.008 and 0.16 gives integers as quotient is-
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
I think the solution will be easier to understand if we rewrite the decimals as fractions:
0.06+=+6%2F100+=+3%2F50
0.008+=+8%2F1000+=+1%2F125
0.16+=+16%2F100+=+4%2F25

Let x be the desired number. Then
  • x divided by 3/50 is an integer.
  • x divided by 1/125 is an integer.
  • x divided by 4/25 is an integer.
Since dividing by a fraction is done by multiplying by the fraction's reciprocal:
  • x times 50/3 is an integer.
  • x times 125/1 is an integer.
  • x times 25/4 is an integer.
If all these multiplications are integers, then the factors of each denominator must be canceled by factors of x. So let's look at the factors of the denominators (of the reciprocals):
3 = 3 * 1
1 = 1 * 1
4 = 2 * 2

Since 1 is a factor of everything, x must only have one 3 and two 2's as factors in order for it to cancel the factors of each of the denominators. (any additional factors will just make x larger.) So:
x = 3 * 2 * 2 = 12