Question

Find the least number which when divided by $12,16,18,30$ leaves remainder $4$ in each case but it is completely divisible by $7?$

Answer 1

$LCMof12,16,18,20=720$
Hence the number can be written in the form $(720\times k+4)$ which is divisible by $7$
If $k=1$, number =$(720\times 1)+4=724$ which is not divisible by $7$
If $k=2$, number =$(720\times 2)+4=1444$ which is not divisible by $7$
If $k=3$, number =$(720\times 3)+4=2164$ which is not divisible by $7$
If $k=4$, number =$(720\times 4)+4=2884$ which is divisible by $7$
Required number = $720\times 4+4=2884$