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 first in, first out(fifo); //

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