Which is the smallest number that can be divided by 15 16 and 21 leaving a reminder of 3

The smallest number will of course be seven; however, you most likely meant the smallest number other than seven.

To meet the criteria stated, n-7 must be a multiple of 15, 21, and 18. Since 0 is a multiple of all numbers, 7 works for this, but to find the second-smallest, we will have to find the smallest number (othed than 0) that is a multiple of all three, the LCM.

We start with the prime factorization of each numbers

15=3×5

21=3×7

18=2×3×3

We now multiply the prime factors together, but factors that multiple numbers have in common ard only counted once. Therefore, the LCM is 2×3×3×5×7. Not that we still multiply by 3 twice because the number 18 has three as a factor twice. However, we don't count it a third our fourth time even though it is a factor of the other numbers. 2×3×3×5×7=630, so 630 is the LCM of 15, 21, and 18. Therefore 637 will have a reminder of 7 when divided by either of them.

answer; i believe the correct answer is (75 years);

if you use only 25 for your entertainment and only 200 for the groceries that you really need and take out the 50 per month for the computer then that should be enough