# 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:

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

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