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6,514 views
20 votes
20 votes

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?

  1. $3047$
  2. $6047$
  3. $7987$
  4. $63847$
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6 Answers

Best answer
26 votes
26 votes

Let $n$ be the smallest number which is divisible by $x, y$ and $z$ and leaves remainder $r$ in each case.

So$, n = LCM ( x , y , z ) + r$

According to Question

$x = 20 , y = 42 ,  z = 76$  and $r = 7$

Smallest number, $n = LCM (20, 42, 76 ) + 7$

$\implies n = 7980 + 7 = 7987$

So, option (C) is the right choice

edited by
11 votes
11 votes

LCM$(20,42,76)$ = $7980$

Remainder is given $7$

NUMBER=$7980$+$7$=$7987$

Option - C $7987$

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