#### Answer

840

#### Work Step by Step

Finding the least common multiple of 2, 3, 4, 5, 6, 7, and 8 can be done using prime factorization, as follows:
1. Factor each number into primes (for example, 6 becomes 2 x 3).
2. For each prime, find the factor where it occurs the most (for example, the prime number 2 occurs the most in the factor of 8, which is 2 x 2 x 2).
3. Multiply the factors where the primes occur the most to find the LCM.
In this case, the factors with the most primes were (2 x 2 x 2) from 8, (3) from 3, (5) from 5, and (7) for 7. (2 x 2 x 2 x 3 x 5 x 7) is equal to 840.