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Question Number 8828 by tawakalitu last updated on 30/Oct/16

If the third common multiple of two number is 495. Find (a) their LCM (b) the second number if one is 15

$$\mathrm{If}\:\mathrm{the}\:\mathrm{third}\:\mathrm{common}\:\mathrm{multiple}\:\mathrm{of}\:\mathrm{two}\:\mathrm{number} \\ $$$$\mathrm{is}\:\mathrm{495}.\:\mathrm{Find} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{their}\:\mathrm{LCM} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{the}\:\mathrm{second}\:\mathrm{number}\:\mathrm{if}\:\mathrm{one}\:\mathrm{is}\:\mathrm{15} \\ $$

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

The third common multiple=LCM×3=495 (a)LCM=((495)/3)=165 (b) If the first number is 15 the second number 11 ..... Continue

$$\mathrm{The}\:\mathrm{third}\:\mathrm{common}\:\mathrm{multiple}=\mathrm{LCM}×\mathrm{3}=\mathrm{495} \\ $$$$\left(\mathrm{a}\right)\mathrm{LCM}=\frac{\mathrm{495}}{\mathrm{3}}=\mathrm{165} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{If}\:\mathrm{the}\:\mathrm{first}\:\mathrm{number}\:\mathrm{is}\:\mathrm{15}\:\mathrm{the}\:\mathrm{second}\:\mathrm{number}\:\mathrm{11}\:..... \\ $$$$\mathrm{Continue} \\ $$

Commented by tawakalitu last updated on 31/Oct/16

i have solve the rest. thanks so much

$$\mathrm{i}\:\mathrm{have}\:\mathrm{solve}\:\mathrm{the}\:\mathrm{rest}.\:\mathrm{thanks}\:\mathrm{so}\:\mathrm{much} \\ $$

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

The 3rd common multiple=LCM×3=495 (a) LCM=((495)/3)=165 (b) If A and B are two numbers then A×B=LCM×GCD (LCM:The least common multiple, GCD:The greatest common divisor) Let G is GCD,we have A=15,LCM=165,B=? 15×B=165×G B=((165G)/(15))=11G For G=1,2,3,...B=11,22,33,44,... General answer B=11G

$$\mathrm{The}\:\mathrm{3rd}\:\mathrm{common}\:\mathrm{multiple}=\mathrm{LCM}×\mathrm{3}=\mathrm{495} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{LCM}=\frac{\mathrm{495}}{\mathrm{3}}=\mathrm{165} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{If}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{are}\:\mathrm{two}\:\mathrm{numbers}\:\mathrm{then} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{A}×\mathrm{B}=\mathrm{LCM}×\mathrm{GCD} \\ $$$$\left(\mathrm{LCM}:\mathrm{The}\:\mathrm{least}\:\mathrm{common}\:\mathrm{multiple},\:\mathrm{GCD}:\mathrm{The}\:\mathrm{greatest}\:\right. \\ $$$$\left.\mathrm{common}\:\mathrm{divisor}\right) \\ $$$$\:\:\:\:\:\mathrm{Let}\:\mathrm{G}\:\mathrm{is}\:\mathrm{GCD},\mathrm{we}\:\mathrm{have}\:\mathrm{A}=\mathrm{15},\mathrm{LCM}=\mathrm{165},\mathrm{B}=? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{15}×\mathrm{B}=\mathrm{165}×\mathrm{G} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{B}=\frac{\mathrm{165G}}{\mathrm{15}}=\mathrm{11G} \\ $$$$\mathrm{For}\:\mathrm{G}=\mathrm{1},\mathrm{2},\mathrm{3},...\mathrm{B}=\mathrm{11},\mathrm{22},\mathrm{33},\mathrm{44},... \\ $$$$\mathrm{General}\:\mathrm{answer}\:\mathrm{B}=\mathrm{11G} \\ $$

Commented by tawakalitu last updated on 31/Oct/16

Wow. God bless you.

$$\mathrm{Wow}.\:\mathrm{God}\:\mathrm{bless}\:\mathrm{you}. \\ $$

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