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-

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 = 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