Divisibility help? I need answer by tomorrow (Sept 17th)?

Using the prime factor method, the smallest integer is 210. Break down each number into its prime factors, and remove the overlapping numbers:
Prime factor for 2 is only 2
For 3, it is only 3
For 7, it is only 7
For 10, the prime factors are 2 and 5 (we will only take 5 from here since 2 already appears above)
For 15, the prime factors are 3 and 5 (we will not take either of these since both appear already above)
For 21, the prime factors are 3 and 7 (again, both have already been counted above).
Hence, the smallest integer is the product of the unique prime factors from above: 2 x 3 x 5 x 7 = 210.
Hope this helps. Good luck.