Find the least number (other than 2) which, when divided by 3, 4, 5, 6, or 7, has a remainder of 2.

422

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842

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2002

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2522

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5102

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Solution

The correct option is E 422
let the number be $x$
we have $x = 3 k + 2$ , $x = 4 a + 2$ , $x = 5 b + 2$ , $x = 6 c + 1$ , $x = 7 d + 1$
So the value of $x$ is $L C M (3, 4, 5, 6, 7) p + 2 = 420 p + 2$
So the least value of $x$ is $420 + 2 = 422$

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