When Louisa arranges her pennies into a rectangle with two equal rows, three equal rows, four equal rows, or six equal rows, she has one leftover penny. When she arranges her pennies into a rectangle with five equal rows, she has two leftover pennies. How many pennies could Louisa have? Remember he has between 10 and 40 pennies total.

The answer must be (a multiple of 2, 3, 4 and 6) + 1, and (a multiple of 5) + 1, because 1 or 2 coins were left over when dividing by 2, 3, 4, 6 or 5.

Let's look at the lowest common multiples of 2, 3, 4, 6:

Prime factorisation:

2 = 2

3 = 3

4 = 2 * 2

6 = 2 * 3

therefore, the lowest common multiple is 2 * 2 * 3 = 12

Let's look at the answers that this would give us (ie multiples of 12):

12 + 1 = 13 <-- this would work, but 11 (ie two less than 13) is not a multiple of 5

12 * 2 + 1 = 25 <-- 23 is not a multiple of 5 either

12 * 3 + 1 = 37 <-- 35 (two less than 37) is a multiple of 5 :)

therefore 37 is our answer since it is one more than a multiple of 12 (ie 36) and two more than a multiple of 5 (ie 35)