The integers from 3 to 7, inclusive are:
{3, 4, 5, 6, 7}
these numbers can be written as multiplication of prime factors as :
{3, 2*2, 5, 2*3, 7}
The smallest common multiple of these numbers must have factors which divide all the factors of these 5 numbers.
So the multiple must have these factors: 3, 2*2 (one two is not enough to divide 4), 5 and 7. We do not need to write 2 and three again, because we already have them.
so the smallest common multiple is 3*2*2*5*7=420
Answer: 420
