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Question 1120812: find the least natural number that has the remainder 3 when divided by 5. the remainder 5 when divided by 7 and the remainder 8 when divided by 10
Answer by greenestamps(13198)   (Show Source):
You can put this solution on YOUR website!
(1) Notice that when the number, n, is divided by each of 5, 7, and 10, the remainder in each case is 2 less than the divisor. That means the number n+2 is divisible by 5, 7, and 10.
The least natural number divisible by 5, 7 and 10 is 70; the number we are looking for is 70-2 = 68.
or...
(2) The number leaves a remainder of 8 when divided by 10; the units digit of the number must be 8.
If the number has units digit 8, and dividing it by 7 leaves a remainder of 5, then 5 less than the number must be a multiple of 7 with units digit 3. The smallest such natural number is 63; the number we are looking for is 63+5 = 68.
And there are numerous other ways you could solve the problem....
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