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

Question #253172

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


1
Expert's answer
2021-10-19T14:39:30-0400

Here

(187)=11,(2110)=11,(2413)=11(18 - 7) = 11, (21 - 10) = 11, (24 - 13) = 11

LCM of 18,2118, 21 and 2424 is 504.504.

Let the required number be 504k11.504k - 11.

Least value of kk for which (504k11)(504k - 11) is divisible by 2323 is k=6k = 6

Required number


=504×611=302411=3013= 504 × 6 - 11 = 3024 - 11 = 3013


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