Find-out-x-y-such-that-lcm-x-y-180-gcd-x-y-45-

Question Number 62242 by Rasheed.Sindhi last updated on 18/Jun/19

Find out x, y such that

lcm (x, y) = 180 \land \gcd (x, y) = 45

Commented by maxmathsup by imad last updated on 19/Jun/19

Δ (x, y) = 45 a n d M (x, y) = 180 \Rightarrow x = 45 u a n d y = 45 v w i t h Δ (u, v) = 1

M (x, y) = 180 \Rightarrow M (45 u, 45 v) = 180 \Rightarrow 45 M (u, v) = 180 \Rightarrow M (u, v) = 4

u . v = M (u, v) . Δ (u, v) = 4 \Rightarrow x y = 45^{2} . 4 \Rightarrow x y = 4 \times 45 \times 45 \dots .

Answered by malwaan last updated on 18/Jun/19

a l w a y s (g c d; l c m) i s a s o l u t i o n

s o (x; y) = (45; 180)

Commented by Rasheed.Sindhi last updated on 18/Jun/19

A p p r e c i a t i o n f o r r a p i d r e s p o n s e!

B u t t h e r e m a y b e o t h e r s o l u t i o n s t o o . T r y

t o f i n d o u t .

Commented by malwaan last updated on 18/Jun/19

f o r t h i s q u e s t i o n

I a m s u r e t h a t i s t h e o n l y s o l u t i o n

b u t I f d = 12 a n d m = 432

w e w i l l g e t t o w s o l u t i o n s

{{12; 432}; {48; 108}}

Commented by Rasheed.Sindhi last updated on 18/Jun/19

{You}^{'} re right sir! I^{'} m sorry for my wrong

viewpoint . Actually I made my question

for multi - solutions but after that I changed

my numbers ignorantly!

Answered by malwaan last updated on 18/Jun/19

a n o t h e r w a y

x = 45 a; y = 45 b

\Rightarrow 45 a b = 180 \Rightarrow a b = 4

\Rightarrow a = 1; b = 4 (c o p r i m e)

\Rightarrow x = 45 \times 1 = 45

; y = 45 \times 4 = 180

∴ (x; y) = (45; 180)

Commented by Rasheed.Sindhi last updated on 18/Jun/19

T h a n k y o u S i r!

Commented by malwaan last updated on 19/Jun/19

m o s t w e l c o m e

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