SOLUTION: Find the smallest number such that if 35 is subtracted from that number the result is exactly divisible by 12, 18, 20, 21, 28 and 30. What is the product of the digits of that numb

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Question 770320: Find the smallest number such that if 35 is subtracted from that number the result is exactly divisible by 12, 18, 20, 21, 28 and 30. What is the product of the digits of that number?
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
N-35 to be perfectly divisible by all those numbers:

12: 2*2*3
18: 2*3*3
20: 2*2*5
21: 3*7
28: 2*2*7
30: 2*3*5

This is like looking for a lowest common denominator. You need 2*2*3*3*5*7.
That product is 1260.
You want %28N-35%29%2FP=M where M is a WHOLE number. The largest number which needs to divide N-35 is listed as 30, so,
%28N-35%29%2F30=1260%2F30,... intuition partly at work here, so difficult to logically explain better, but find N.