Question

Afla cel mai mic numar care impartit la 12,18, 40 sa dea respectiv 11,17 si 39

Answer 1

a:12=b r 11
a:18=c r 17
a:40=d r 39
D=I×C+R
a=12×b+11
a=18×c+17
a=40×d+39
adunam la toate cate 1, si avem
a+1=12×b+12
a+1=18×c+18
a+1=40×d+40
dam factor comun
a+1=12(b+1)
a+1=18(c+1)
a+1=40(d+1)
=> a este cel mai mic multiplu comun al numerelor 12, 18, 40.
[12,18,40]=2^3×3^2×5=72×5=360
12=2^2×3
18=3^2×2
40=5×2^3
a+1=360+1
=361