Three devices A; B ;C shine like that: A shines every 25 minutes B shines every 30 minutes C shines every 35 minutes. The three devices shined simultaneous, (at the same time) at 10 pm. At which time will they shine simultaneous for the first time after midnight?


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Question Number 133772 by mathocean1 last updated on 24/Feb/21

$T h r e e d e v i c e s A; B; C s h i n e l i k e t h a t :$ $A s h i n e s e v e r y 25 m i n u t e s$ $B s h i n e s e v e r y 30 m i n u t e s$ $C s h i n e s e v e r y 35 m i n u t e s .$ $T h e t h r e e d e v i c e s s h i n e d s i m u l t a n e o u s,$ $(a t t h e s a m e t i m e) a t 10 p m .$ $A t w h i c h t i m e w i l l t h e y s h i n e s i m u l t a n e o u s$ $f o r t h e f i r s t t i m e a f t e r m i d n i g h t ?$
	Answered by TheSupreme last updated on 24/Feb/21

	$N = k_{1} 5^{2} = k_{2} 6 \times 5 = k_{3} 7 \times 5$ $N_{m i n} = m c m (5^{2}, 3 \times 2, 7) / 60 = \frac{5^{2} \times 3 \times 2 \times 7}{3 \times 2^{2} \times 5} = 35 / 2 = 17.5 h$ $10 : 00 p m$ $27.30 p m$ $3.30 p m$
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