Question

46) The hundreds digit of the smallest six-digit number divisible by 12, 13,
14, 15 and 16 is

Answer 1

Answer: 2

Explanation:

`12=2^2 * 3\\\\13=13\\\\14=2 * 7\\\\15=3 * 5\\\\16 =2^4\\\\\therefore \lcm(12, 13, 14, 15, 16)=2^4 * 3 * 5 * 7 * 13=21840`

Multiplying this by 5 to make it the smallest possible six-digit number, we get 109200, meaning the hundreds digit is 2.