could anyone please find a solution to that problem:
$b$,$c$,$d$ are consecutive even integers such that $2\lt b \lt c \lt d$. what is the largest positive integer that MUST be a divisor of $bcd$?
2026-03-27 20:30:41.1774643441
number system and divisibility
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At least one of the numbers is even and at least one is a multiple of 4. Also one is a multiple of 3. So the product must be divisible by 48. Take $b=4,c=6,d=8$ then the product is 192=48\times4. Take $b=10,c=12,d=14$, then the product is $1680=48\times 35$. They have greatest common factor 48, so 48 is the best possible result.