The largest number of five digits which, when divided by 16, 24, 30 or 36 leaves the same remainder 10 in each case is:

99370

LCM of 16, 24, 30, 36 = 720

The largest number of five digits = 99999

After dividing 99999 by 720, the remainder = 639

∴ The largest five digit number divisible by 720 = 99999 - 639 = 99360

Required number = 99360 + 10 = 99370