The least number which when divided by 4, 6, 8 and 9 leaves zero remainder in each case and when divided by 13 leaves a remainder of 7 is:

72

Since we are looking for the number that leaves 0 as remainder with 4, 6, 8 and 9, we are actually looking for the LCM.

LCM of 4, 6, 8 and 9  =2 × 2 × 2 × 3 × 3 = 72

\(\frac{72}{13}\) = 7 remainder

So, the answer is 72