find pairs of natural numbers whose LCM is 78 and GCD is 13

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Solution

Dear student
$L e t t h e n u m b e r b e x a n d y w e k n o w t h a t L C M \times G C D = x y \Rightarrow 78 \times 13 = x y \Rightarrow x y = 1014 \Rightarrow x y = 2 \times 3 \times 13 \times 13 S i n c e G C D i s 13 T h e r e f o r e 13 s h o u l b b e m u l t i p l e o f b o t h n u m b e r s i . e ., 2 \times 13 a n d 3 \times 13 S o t h e n u m b e r s a r e x = 26 a n d y = 39 .$
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Similar questions

78

13

a_{1}, b_{1}, c_{1}

a_{2} = g c d (b_{1}, c_{1}), b_{2} = g c d (c_{1}, a_{1}), c_{2} = g c d (a_{1}, b_{1}),

a_{3} = l c m (b_{2}, c_{2}), b_{3} = l c m (c_{2}, a_{2}), c_{3} = l c m (a_{2}, b_{2}) .

g c d (b_{3}, c_{3}) = a_{2}

56

6

216 ?

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