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Question Number 146470 by mathdanisur last updated on 13/Jul/21

$$if4a=7b=2cand\mathit{d}\mathit{c}\mathit{m}(a;b;c)=3$$$$finda+b+c=?$$

Answered by Rasheed.Sindhi last updated on 13/Jul/21

$$if4a=7b=2cand\mathit{g}\mathit{c}\mathit{d}(a,b,c)=3$$$$a+b+c=?$$$$a=\frac{1}{2}c,b=\frac{2}{7}c$$$$\because a,b,c\in \mathbb{N}$$$$\therefore 2\mid c\mathrm{\&}7\mid c$$$$Also\mathit{g}\mathit{c}\mathit{d}(a,b,c)=3$$$$\therefore 3\mid c$$$$c=2\times 3\times 7=42$$$$a=21$$$$b=12$$$$a+b+c=21+12+42=75$$$$Verification:$$$$4\left(21\right)=7\left(12\right)=2\left(42\right)=84$$$$\mathit{g}\mathit{c}\mathit{d}(21,12,42)=3$$

Commented by mathdanisur last updated on 13/Jul/21

$$thankyouSercool$$

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