Question

What is the least number which when divided by $4,6,8$ and $9$ leaves zero remainder in each case but when divided by $13$ leaves a remainder of $7$ ?

Answer 1

LCM of $4,6,8$ and$9$ = $72$
Now,
$72÷4=18$ (no remainder)
$72÷6=12$ (no remainder)
$72÷8=9$ (no remainder)
$72÷9=8$ (no remainder)
Now,
When the number is divided by $13$ leaves a remainder of $7$.
$72$ when divided by $13$ gives remained $7$ as:
$72=13\times 5+7$.
$\therefore$ The least number which when divided by $4,6,8$ and $9$ leaves zero remainder, and when divided by $13$ leaves a remainder of $7$ is $72$