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MATH / The least common multiple of 1!+2!, 2!+3!, 3!+4!, 4!+5!, 5!+6!, 6!+7!, 7!+8!, and 8!+9! can be expressed in the form a⋅b!, where a and b are integers and b is as large as possible.…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

The least common multiple of 1!+2!1!+2!, 2!+3!2!+3!, 3!+4!3!+4!, 4!+5!4!+5!, 5!+6!5!+6!, 6!+7!6!+7!, 7!+8!7!+8!, and 8!+9!8!+9! can be expressed in the form a⋅b!a\cdot b!, where aa and bb are integers and bb is as large as possible. What is a+ba+b?
Plain-text mathematical notation (without MathML)
The least common multiple of 1!+2!, 2!+3!, 3!+4!, 4!+5!, 5!+6!, 6!+7!, 7!+8!, and 8!+9! can be expressed in the form a⋅b!, where a and b are integers and b is as large as possible. What is a+b?
Original LaTeX notation
The least common multiple of $1!+2!$, $2!+3!$, $3!+4!$, $4!+5!$, $5!+6!$, $6!+7!$, $7!+8!$, and $8!+9!$ can be expressed in the form $a\cdot b!$, where $a$ and $b$ are integers and $b$ is as large as possible. What is $a+b$?

level

Level 5

type

Number Theory

Discussion

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Source and history

task_id
74b421d3-2299-5c6e-a987-dbb379d82f55
task_key
number~5ftheory--test--74b421d3-2299-5c6e-a987-dbb379d82f55
task_revision_id
1
config / split
number_theory / test

Official source

initial import