Answer to Question #253172 in Combinatorics | Number Theory for Benjamin

Question

Find the least multiple of 23, which when divided by 18, 21, and 24 leaves the remainder 7,10 and 13 respectively.

Answer 1

Here

$$(18 - 7) = 11, (21 - 10) = 11, (24 - 13) = 11$$

LCM of $18, 21$ and $24$ is $504.$

Let the required number be $504k - 11.$

Least value of $k$ for which $(504k - 11)$ is divisible by $23$ is $k = 6$

Required number

$$= 504 × 6 - 11 = 3024 - 11 = 3013$$