Over the next two days, Columbia Employment Agency is interviewing clients who wish to find jobs. On the first day, the agency plans to interview clients in groups of 8 . On the second day, the agency will interview clients in groups of 7 . If the employment agency will interview the same number of clients on each day, what is the smallest number of clients that could be interviewed each day?

The smallest number of clients that could be interviewed each day can be found by determining the least common multiple (LCM) of 8 and 7. The LCM of two numbers is the smallest multiple that they both share. For 8 and 7, since they have no common factors besides 1, you can calculate the LCM by multiplying them together: 8 × 7 = 56. So, the smallest number of clients that could be interviewed each day is 56. This means on the first day, 56 clients would be interviewed in groups of 8 (resulting in 7 groups), and on the second day, the same number of clients would be interviewed in groups of 7 (resulting in 8 groups). If you're ever in doubt or need to find the LCM, remember that listing multiples or using the prime factorization method are effective techniques!