Question 1120812
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(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.<br>
The least natural number divisible by 5, 7 and 10 is 70; the number we are looking for is 70-2 = 68.<br>
or...
(2) The number leaves a remainder of 8 when divided by 10; the units digit of the number must be 8.<br>
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.<br>
And there are numerous other ways you could solve the problem....