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The least common multiple of 1!+2!+3!, 2!+3!+4!, 3!+4!+5!, 4!+5!+6!, 5!+6!+7!, 6!+7!+8!, 7!+8!+9!, and 8!+9!+10! 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?

 Nov 20, 2020
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lcm(1! + 2! + 3!, 2! + 3! + 4!, 3! + 4! + 5!, 4! + 5! + 6!, 5! + 6! + 7!, 6! + 7! + 8!, 7! + 8! + 9!, 8! + 9! + 10!)

 

=4,572,288,000=2,286,144,000  x  2

 

(b, a) =[2,286,144,000,  2]

 

[b + a] =[2,286,144,000  +  2] =2,286,144,002

 Nov 20, 2020

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