# Seven numbers

Write seven 4-digit numbers that are divisible by 3 and at the same time by 4.

Result

a1 =  1008
a2 =  1020
a3 =  1032
a4 =  1044
a5 =  1056
a6 =  1068
a7 =  1080

#### Solution:

$3 \ ... \ prime number \ \\ 4=2^2 \ \\ LCM(3, 4)=2^2 \cdot 3=12 \ \\ \ \\ d=LCM(3,4)=12 \ \\ b=1000/d=1000/12 \doteq \dfrac{ 250 }{ 3 } \doteq 83.3333 \ \\ b_{1}=\lceil b \rceil=\lceil 83.3333 \rceil=84 \ \\ \ \\ a_{1}=b_{1} \cdot \ d=84 \cdot \ 12=1008$
$a_{2}=a_{1}+d=1008+12=1020$
$a_{3}=a_{2}+d=1020+12=1032$
$a_{4}=a_{3}+d=1032+12=1044$
$a_{5}=a_{4}+d=1044+12=1056$
$a_{6}=a_{5}+d=1056+12=1068$
$a_{7}=a_{6}+d=1068+12=1080$

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