Question

find the least number when divided by 15,16,24,36 leaves remainder 7 in each case​

Answer 1

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

$\fbox{Prime\;factorization\;method}$

$\begin{array}{r | l} 2 & 12 \\ \cline{2-2} 2 & 6 \\ \cline{2-2} & 3\end{array}$

$\begin{array}{r | l} 2 & 16 \\ \cline{2-2} 2 & 8 \\ \cline{2-2} 2 & 4 \\ \cline{2-2} & 2 \end{array}$

$\begin{array}{r | l} 2 & 24 \\ \cline{2-2} 2 & 12 \\ \cline{2-2} 2 & 6 \\ \cline{2-2} & 3 \end{array}$

$\begin{array}{r | l} 2 & 36 \\ \cline{2-2} 2 & 18 \\ \cline{2-2} 3 & 9 \\ \cline{2-2} & 3 \end{array}$

LCM = 2 × 2 × 2 × 2 × 3 × 3

LCM = 144

$\fbox{Adding\;remainder\;7\;to\;the\;LCM}$

= 144 + 7

= 151

$\large{\fbox{The\;least\;number\; is\;151}}$

$\Large{\boxed{\sf\:{Additional\; Information}}}$

In case :-

★Three positive integers a,b,c

★HCF(a,b,c) × LCM(a,b,c) ≠ a × b × c

$\tt{\rightarrow LCM(a,b,c)=\dfrac{a\times b\times c\times HCF (a,b,c)}{HCF(a,b)\times HCF(b,c)\times HCF(a,c)}}$

$\tt{\rightarrow HCF(a,b,c) =\dfrac{a\times b\times c\times LCM (a,b,c)}{LCM(a,b)\times LCM(b,c)\times LCM(a,c)}}$