Find the least number which when divided by 25 and 30 leaves 10 as remainder

Hint: First of all let the least number be N. Then using the division theorem, N = dq + r, write, N = 25a + 9, N = 40b + 9 and N = 60c + 9. Find N by taking LCM of 25, 40 and 9 and adding 9 to it.

“Complete step-by-step answer:”
Here, we have to find the least number which when divided by 25, 40 and 60 leaves 9 as the remainder in each case.
Before solving this question, we must know what division theorem is. Division theorem states that “If ‘n’ is any integer and ‘d’ is a positive integer, there exist unique integers ‘q’ and ‘r’ such that,
$n=dq+r$ where 0${\leq}$r