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Question Number 8829 by tawakalitu last updated on 30/Oct/16

The LCM of three whole number is 144. what is their third common multiple.

$$\mathrm{The}\:\mathrm{LCM}\:\mathrm{of}\:\mathrm{three}\:\mathrm{whole}\:\mathrm{number}\:\mathrm{is}\:\mathrm{144}.\: \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{their}\:\mathrm{third}\:\mathrm{common}\:\mathrm{multiple}. \\ $$

Commented by Rasheed Soomro last updated on 31/Oct/16

All the common multiples are multiples of LCM. First common multiple is LCM itself. The second common multiple is LCM×2, the 3rd common multiple is LCM×3 etc. So the third common multiple here is 144×3=432

$$\mathrm{All}\:\mathrm{the}\:\mathrm{common}\:\mathrm{multiples}\:\mathrm{are}\:\mathrm{multiples}\:\mathrm{of}\:\mathrm{LCM}. \\ $$$$\mathrm{First}\:\mathrm{common}\:\mathrm{multiple}\:\mathrm{is}\:\mathrm{LCM}\:\mathrm{itself}.\:\mathrm{The}\:\mathrm{second} \\ $$$$\mathrm{common}\:\mathrm{multiple}\:\mathrm{is}\:\mathrm{LCM}×\mathrm{2},\:\mathrm{the}\:\mathrm{3rd}\:\mathrm{common}\:\mathrm{multiple} \\ $$$$\mathrm{is}\:\mathrm{LCM}×\mathrm{3}\:\mathrm{etc}. \\ $$$$\mathrm{So}\:\mathrm{the}\:\mathrm{third}\:\mathrm{common}\:\mathrm{multiple}\:\mathrm{here}\:\mathrm{is}\:\mathrm{144}×\mathrm{3}=\mathrm{432} \\ $$

Commented by tawakalitu last updated on 31/Oct/16

Thanks sir. God bless you.

$$\mathrm{Thanks}\:\mathrm{sir}.\:\mathrm{God}\:\mathrm{bless}\:\mathrm{you}. \\ $$

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