Question

The HCF and LCM of two numbers are 135 and 810 respectively if one number is 405 then what is other number

Answer 1

Answer:

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Answer 2

$\frak{Given}\:\begin{cases} \:\quad \sf H.C.F \:of \:two \:number \:is\:=\:\pmb{\frak{ 135}}\:.\:\\\:\quad \sf L.C.M \:of \:two \:number \:is\:=\:\pmb{\frak{ 810}}\:.\:\\\:\quad \sf One\: \:of \:the\:number \:is\:=\:\pmb{\frak{ 405}}\:.\:\end{cases}$

Need To Find : The Other Number ?

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀

❍ Let's say that , Other Number be x .

$\pmb{\underline {\dag\:\frak{ \:As\:We\:Know\:that\:\::\:}}}$

$\qquad \star \:\pmb{\underline {\boxed { \: \sf\: Product \:of \:two \:Numbers \:=\:\Big\{ \:H.C.F\:\Big\}\:\times\:\Big\{\:L.C.M\:\Big\}\:}}}$

$\dag\:\underline {\frak { Putting \:known \:Values \:in \:Given \:Formula \:\::\:}}$

$\twoheadrightarrow \:\sf Product \:of \:two \:Numbers \:=\:\Big\{ \:H.C.F\:\Big\}\:\times\:\Big\{\:L.C.M\:\Big\}\: \\\\\\ \twoheadrightarrow \:\sf \;\:\Big\{ \:405\:\Big\}\:\times\:\Big\{\:x\:\Big\}\: \:=\:\Big\{ \:810\:\Big\}\:\times\:\Big\{\:135\:\Big\}\: \\\\\\ \twoheadrightarrow \:\sf \;\:\Big\{ \:405\:\times\:x\:\Big\}\: \:=\:\Big\{ \:810\:\times\:135\:\Big\}\: \\\\\\ \twoheadrightarrow \:\sf \;\:\Big\{ \:405x\:\Big\}\: \:=\:\Big\{ \:109350\:\Big\}\: \\\\\\ \twoheadrightarrow \:\sf \:405x\:\: \:= \:109350\: \\\\\\\twoheadrightarrow \:\sf \:x\:\: \:= \:\cancel {\dfrac{109350}{405}}\: \\\\\\ \twoheadrightarrow \pmb {\underline {\boxed {\purple {\:\frak{ \:x\:\:=\:270\:}}}}}\:\bigstar \:$

∴ Hence ,  The other number is 270 .