One day, Jasmine and her friends had lunch while sitting at tables of 13. Another day, they had lunch at tables of 5. What is the smallest number of people that could be in the group?
since 5 and 13 share no factors, they must be 5*13 = 65 people.
To find the smallest number of people that could be in the group, we need to find the least common multiple (LCM) of 13 and 5.
The LCM is the smallest multiple that two or more numbers have in common. We can find the LCM by finding the multiples of each number until we find a common multiple.
For 13: 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, 143, 156, 169
For 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65
From the list of multiples, we can see that 65 is the first common multiple of both 13 and 5. Therefore, the smallest number of people that could be in the group is 65.