Question

Q-18 What is the smallest number that when divided separately by 20 and 48
gives the remainder of 7 every time?​

Answer 1

AnswEr :

247.

$\bf{\green{\large{\underline{\underline{\bf{Given\::}}}}}}$

When divided separately by 20 and 48 gives the remainder of 7 every time.

$\bf{\red{\large{\underline{\underline{\bf{To\:find\::}}}}}}$

The smallest number.

$\bf{\purple{\large{\underline{\underline{\bf{Explanation\::}}}}}}$

We have to find the L.C.M of 20 and 48.

$\begin{array}{r|l}2&20,48\\ \cline{2-2} 2& 10,24\\ \cline{2-2} 2& 5,12\\ \cline{2-2}2& 5,6\\ \cline{2-2} 3& 5,3\\ \cline{2-2} 5&5,1\\ \cline{2-2} &1,1\end{array}$

∴ L.C.M = 2 × 2 × 2 × 2 × 3 × 5 = 240.

$\bf{\orange{\large{\underline{\underline{\bf{\blacksquare{Required\:smallest\:Number\::}}}}}}}$

$\longrightarrow\sf{Smallest\:Number\:=\:240+7}\\\\\\\longrightarrow\sf{\pink{Smallest\:Number\:=\:247}}$