William W. answered • 05/07/19

Experienced Tutor and Retired Engineer

Start at the back of the process by considering the integer that gets divided by 3 and gets a remainder of 2. The smallest number that gets a remainder of 2 when divided by 3 is 5 (5/3 = 1 with remainder 2).

Now consider the integer that gets divided by 5 and has a remainder of 3. You want the quotient to be 5 (5 is needed to get a remainder of 2 in the previous work) and you want the remainder to be 4 so 5 * 5 + 4 = 29.

Now consider the integer that gets divided by 6 and has a remainder of 4. You want the quotient to be 29 and the remainder to be 4 so 29 * 6 + 4 = 178.

The number is 178.

Check:

178/6 = 29 remainder 4

29/5 = 5 remainder 4

5/3 = 1 remainder 2