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Question Number 104536 by Anindita last updated on 22/Jul/20

$$\mathbf{The}\mathbf{sum}\mathbf{of}\mathbf{two}\mathbf{numbers}\mathbf{is}384\mathbf{and}$$$$\mathrm{t}\mathbf{heir}\mathbf{GCD}\mathbf{is}48.\mathbf{What}\mathbf{is}\mathbf{the}\mathbf{LCM}\mathbf{of}$$$$\mathbf{the}\mathbf{numbers}?$$

Commented by 1549442205PVT last updated on 22/Jul/20

$$\mathrm{Similar}\mathrm{to}\mathrm{Q}104413$$

Answered by mr W last updated on 22/Jul/20

$$gcd(x,y)=48$$$$\Rightarrow x=48m$$$$\Rightarrow y=48n$$$$withgcd(m,n)=1...\left(i\right)$$$$x+y=48(m+n)=384$$$$\Rightarrow m+n=8...\left(ii\right)$$$$lcm(x,y)=48\times lcm(m,n)$$$$$$$$case1:m=1,n=7orm=7,n=1$$$$lcm(x,y)=48\times lcm(1,7)=336$$$$case2:m=3,n=5orm=5,n=3$$$$lcm(x,y)=48\times lcm(3,5)=720$$$$$$$$sotheansweris336or720.$$

Commented by Rasheed.Sindhi last updated on 22/Jul/20

$$\mathcal{G}\stackrel{\mathcal{R}}{}\mathcal{E}\stackrel{\mathcal{A}}{}\mathcal{T}!$$

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