GATE 2018 CS – Question 4
What would be the smallest natural number which when divided either by 20 or by 42 or by 76 leaves a remainder of 7 in each case?
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Correct answer: (C) 7987
Explanation
The number is $\text{LCM}(20,42,76)+7$. $20=2^2\cdot5$, $42=2\cdot3\cdot7$, $76=2^2\cdot19$, so the LCM is $4\cdot3\cdot5\cdot7\cdot19=7980$ and the number is $7987$.