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:

85 78 65 72

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