What is the smallest number that can be divided evenly by all the digits from 2 to 9?

The least common multiple of the numbers

... 2, 3, 2², 5, 2·3, 7, 2³, 3² . . . . . . prime factorization of numbers 2–9

will be 2³·3²·5·7 = 2520

Note that the factors of the LCM are the highest powers of the prime factors of the individual numbers. The highest power of 2 is 3; the highest power of 3 is 2, so 2³ and 3² are included as factors of the LCM.

The smallest number divisible by the integers 2–9 is 2520.