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AMC (AIMO validation set) / https://artofproblemsolving.com/wiki/index.php/2022_AMC_12A_Problems/Problem_4 / The least common multiple of a positive integer n and 18 is 180, and the greatest common divisor of n and 45 is 15. What is the sum of the digits of n?

Problem

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problem

The least common multiple of a positive integer

n

and

18

180

, and the greatest common divisor of

n

and

45

15

. What is the sum of the digits of

n

Plain-text mathematical notation (without MathML)

The least common multiple of a positive integer n and 18 is 180, and the greatest common divisor of n and 45 is 15. What is the sum of the digits of n?

Original LaTeX notation

The least common multiple of a positive integer $n$ and $18$ is $180$, and the greatest common divisor of $n$ and $45$ is $15$. What is the sum of the digits of $n$?

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Source and history

upstream_id / Original problem ID: https://artofproblemsolving.com/wiki/index.php/2022_AMC_12A_Problems/Problem_4
task_id: be2fea53-bad8-58bf-9d0f-16530ecf87c1
task_key: default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12A~5fProblems~2fProblem~5f4
task_revision_id: 2
config / split: default / train

Official source

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