Question

on a morning walk,three persons step off together and their steps measure 40cm ,42cm,and 45cm respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps ?

Answer 1

answer is in image....

Answer 2

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

★Here we have to find LCM of 40,42 and 45

★40 :-

$\begin{array}{r | l} 2 & 40 \\ \cline{2-2} 2 & 20 \\ \cline{2-2} 2 & 10 \\ \cline{2-2} & 5 \end{array}$

= (2)³ × 5

★42 :-

$\begin{array}{r | l} 2 & 42 \\ \cline{2-2} 3 & 21 \\ \cline{2-2} & 7 \end{array}$

★45 :-

$\begin{array}{r | l} 3 & 45 \\ \cline{2-2} 3 & 15 \\ \cline{2-2} & 5 \end{array}$

= (3)² × 7

LCM(40,42,45) = (2)³ × (3)² × 5 × 7

= 840 × 3

= 2520

${\boxed{\sf\:{Distance\;Covered\;each\;is\;2520}}}$

$\boxed{\begin{minipage}{11 cm} Verification \\ \\ \ 1st\;step=\dfrac{2520}{40}=63 \\ \\ 2nd\;step=\dfrac{2520}{42}=60 \\ \\ 3d\;step=\dfrac{2520}{45}=56 \end{minipage}}$