How many positive integers less than $1,000$ are multiples of $5$ and are equal to $3$ times an even integer?
It is simply asking for multiples of $5$ and $6$
Is there a way to do this without guessing or counting? This is from the SAT.
I have tried it, but I counted all, and found common ones, the answer was $33$.
Best Answer
If it's a multiple of two numbers it is a multiple of the least common mutliple, in this case the least common multiple of $6$ and $5$ is $30$. You now want to find how many multiples of $30$ are under $1000$
Hint: $33(30)=990,34(30)=1020$