Question

Find the least number which when divided by 25, 40 and 60 leaves 9 as the remainder in each case.

Answer 1

25, 40 and 60 exactly divides the least number that is equal to their LCM.
So, the required number that leaves 9 as a remainder will be LCM + 9.

Finding the LCM:

$\begin{array}{l}2\overline{)25,40,60}\\ 2\overline{)25,20,30}\\ 2\overline{)25,10,15}\\ 3\overline{)25,5,15}\\ 5\overline{)25,5,5}\\ 5\overline{)\text{5, 1, 1}}\\ \text{1, 1, 1}\end{array}$
LCM = 2³ × 3 × 5² = 600
∴ Required number = 600 + 9 = 609