Question

find the least number of five digits exactly divisible by 16, 18, 24 and 36

Answer 1

    2 | 36,24,18,16
    3  |18, 12, 9,  8
    3  | 6,   4,  3,  8
    2  | 2,   4,  1,  8
    2  | 1,   2,   1, 4
         1,   1,   1, 2

The LCM of 16,18,24,36 : 2 x 2 x 2 x 2 x 3 x 3 = 144
Smallest 5 digit number = 10,000
10,000 / 144 = 69.44
70 * 144 = 10,080
The required number is 10,080

Answer 2

LCM of 16, 18, 24, 36  =  144

reminder of 10,000 / 144 = 64
Add (144-80) to the number 10,000.              So answer is 10,080