Question 1013192
The numbers 3,5,qnd 7 are prime numbers.
If a number is a multiple of 3, 5, and 7,
each of those prime numbers appears at least once in the prime factorization of the number.
The number is going to be {{{3*5*7*something}}} .
In other words, it must be a multiple of {{{3*5*7=105}}} .
{{{5000/105=47.6}}} (rounded),
so the numbers you are looking for are
{{{1*105=105}}}
{{{2*105=210}}}
{{{3*105=315}}}
 and so on, all the way up to
{{{47*105=4935}}} .
There are obviously {{{highlight(47)}}} common multiples of 3, 5 and 7 between 1 and 5000.