Question

find the smallest number which when divided by 12,20and 36 will leave a remainder of 7 in each case​

Answer 1

AnswEr :

187.

$\bf{\pink{\underline{\underline{\sf{Given\::}}}}}$

When divided by 12, 20, and 36 will leave a remainder of 7 in each case.

$\bf{\pink{\underline{\underline{\sf{To\:find\::}}}}}$

The smallest number.

$\bf{\pink{\underline{\underline{\sf{Explanation\::}}}}}$

We get Taking L.C.M of 12, 20, and 36 :

$\begin{array}{l|r}2& 12,20,36\\ \cline{2-2} 2 & 6,10,18\\ \cline{2-2} 3& 3,5,9\\ \cline{2-2} 3& 1,5,3\\ \cline{2-2} 5& 1,5, 1 \\ \cline{2-2} & 1,1,1\end{array}}$

∴ L.C.M. = 2 × 2 × 3 × 3 × 5 = 180.

So,

The smallest number required  = 180 + 7 = 187.

$\boxed{\begin{minipage}{6 cm} \underline{Full - Form of L.C.M and H.C.F\::}\\ \\ {\sf L.C.M.=Lowest\:Common\:Multiple} \\ \\ \sf{H.C.F.=Highest\:Common\:Factor}\: \end{minipage}}$

Answer 2

$</p><p>\huge{\pink{\tt{Hello!!! }}}$

$</p><p>\huge {\fbox{\fbox{\rightarrow {\mathfrak {\green{QUESTION \: - }}}}}}$

- Find The Smallest Number Which When Divided By 12, 20 and 36 Will Leave A Remainder of 7 In Each Case -

$</p><p>\huge {\fbox{\fbox{\rightarrow {\mathfrak {\blue{ANSWER\: - \: 187 }}}}}}$

$</p><p>\huge {\fbox{\fbox{\rightarrow {\mathfrak {\red{SOLUTION\: - }}}}}}$

• Find The LCM I.e, Least Common Multiple of 12, 20 and ,30

• Add 7 To The LCM to get the required Answer.

Calculating, we get the LCM to be 180.

Adding 7, The Final Answer Becomes 187.