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The least number which when divided by 25, 40 and 60 leaves 9 as the remainder in each case is
The number minus 9 must be a common multiple of 25, 40 and 60, so we take their LCM. Since $$25 = 5^2$$, $$40 = 2^3 \times 5$$ and $$60 = 2^2 \times 3 \times 5$$, the LCM is $$2^3 \times 3 \times 5^2 = 600$$. The required number is $$600 + 9 = 609$$.
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