Question

29
Given that HCF (306, 657)=9, find LCM (306, 657).​

Answer 1

Given : The [ Highest Common Factor ] H.C.F of 306 and 657 is 9 .

Exigency To Find : [ Lowest Common Factor ] L.C.M of 306 and 657 .

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

⠀⠀⠀⠀⠀❍ Finding L.C.M :

$\dag\:\:\sf{ As,\:We\:know\:that\::}$

$\qquad \dag\:\:\bigg\lgroup \sf{ Product \:of\:two\:numbers \:\:= \: H.C.F \:\times L.C.M }\bigg\rgroup$

⠀⠀⠀⠀⠀Here , Two numbers are 306 & 657 and H.CF is 9 .

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}$

$\qquad:\implies \sf 306 \: \times 657 \:= \:9 \times L.C.M$

$\qquad:\implies \sf \dfrac{306 \: \times 657}{9} \:= \: L.C.M$

$\qquad:\implies \sf \dfrac{201042}{9} \:= \: L.C.M$

$\qquad:\implies \sf \cancel {\dfrac{201042}{9}} \:= \: L.C.M$

$\qquad:\implies \sf 223388 \:= \: L.C.M$

$\qquad:\implies \underline {\purple {\frak L.C.M \:\:= \:223388 \:}}\:\:\bigstar$

Therefore,

$\qquad \therefore \:\underline {\sf L.C.M \:\:of \:\:306\:\& \:\:657 \:\:is\:\:\bf 223388 }$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀