find the lowest number between 200 and 500 which leaves a remainder of 3 in each case which will divisible by 8 , 10, 12 and 30?


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Question Number 135990 by zakirullah last updated on 17/Mar/21

$f i n d t h e l o w e s t n u m b e r b e t w e e n 200 a n d 500 w h i c h$ $l e a v e s a r e m a i n d e r o f 3 i n e a c h c a s e$ $w h i c h w i l l d i v i s i b l e b y 8, 10, 12 a n d 30 ?$
	Answered by Olaf last updated on 17/Mar/21
	$N = 8k+3 = 10l+3 = 12m+3 = 30n+3 200≤N≤500 ⇒ 7≤n≤16 12m+3 = 30n+3 ⇒ 5n = 2m ⇒ n∈{8, 10,12, 14, 16} N_(min) = 30.8+3 = 243 = 12.20+3 = 10.24+3 = 8.30+3$
	$N = 8 k + 3 = 10 l + 3 = 12 m + 3 = 30 n + 3$ $200 ⩽ N ⩽ 500 \Rightarrow 7 ⩽ n ⩽ 16$ $12 m + 3 = 30 n + 3 \Rightarrow 5 n = 2 m$ $\Rightarrow n \in {8, 10, 12, 14, 16}$ $N_{m i n} = 30.8 + 3 = 243 = 12.20 + 3 = 10.24 + 3 = 8.30 + 3$
	Commented by zakirullah last updated on 18/Mar/21

	$y o u a r e r i g h t d e a r s i r! b u t h o w c a n i u n d e r s t a n d$ $c h i l d r e n o f c l a s s 6 t h .$ $s i r c a n y o u d o t h i s o n s i m p l e m e t h o d ?$
	Answered by mr W last updated on 18/Mar/21

	$L C M f r o m 8 a n d 12 i s 24 .$ $L C M f r o m 24 a n d 30 i s 120 .$ $s u c h a n u m b e r i s a m u l t i p l e o f 120$ $p l u s 3, i . e . 123, 243, 363 e t c .$ $s m a l l e s t b e t w e e n 200 a n d 500 i s 243 .$ $l a r g e s t b e t w e e n 200 a n d 500 i s 483 .$
	Commented by otchereabdullai@gmail.com last updated on 18/Mar/21

	$powerful!$
	Commented by zakirullah last updated on 18/Mar/21

	$ok welldon$
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