Question

Find the smallest number which when divided by 15, 25 and 30 leaves 8 as the remainder in each case​

Answer 1

$First \:we \: have \: to \:find \: LCM \: of$

$15, 25 \:and \: 30 , we \:get$

5 | 15 ,25 ,30

_____________

3 |3 , 5 , 6

_____________

*** 1 , 5 , 2

LCM of 15,25 and 30 = 5 × 3 × 5 × 2

= 150

Required reminder = 8

$\red{ The \: smallest \: number \: which \:when}$

$\red{divided \:by \: 15, 25 \:and \:30 \: leave \:8}$

$\red{as \:the \: Remainder \: in \:each \:case}$

$\blue {= LCM( 15,25,30) + Remainder }$

$= 150 + 8$

$\green{ = 158}$

•••♪

Answer 2

$\huge\bf\underline\red{Question :}$

$\sf\green{Find \ the \ smallest \ number \ which \ when}$

$\sf\green{divided \ by \ 15, \ 25 \ and \ 30 \ leaves \ 8 \ as \ the }$

$\sf\green{remainder \ in \ each \ case}$

$\huge\bf\underline\orange{Solution :}$

$\sf\blue{First \:we \: have \: to \:find \: LCM \: of \: 15,\: 25 \:and \: 30 ,\: we \:get }$

$\sf\begin{array}{r | l}</p><p></p><p>5 & 15,25,30 \\</p><p></p><p></p><p></p><p>\cline{2-2} 3 & 3,5,6 \\</p><p></p><p></p><p>\cline{2-2} & 1,5,2</p><p></p><p>\end{array}$

$\sf\purple{LCM \ of \ 15, \ 25 \ and \ 30 \ = \ 5 × 3 × 5 × 2 \ = \ 150}$

$\sf\blue{Required \ reminder \ = \ 8}$

$\sf\purple{ The \: smallest \: number \: which \:is \:divided \:by \: 15, 25 \:and \:30 \: leave \:8}$

$\sf\blue{As \:the \: Remainder \: in \:each \:case}$

$\sf\purple {\longrightarrow\:\:\:\ LCM \ ( 15,25,30) \ + \ Remainder }$

$\sf\blue{ \longrightarrow\:\:\: \ 150 + 8}$

$\sf\purple{ \longrightarrow\:\:\:\ 158}$