Final answer:
Keisha must choose the number 84, as it is the only number between 61 and 107 that is a multiple of 4, 7, and 14.
Step-by-step explanation:
To find the numbers between 61 and 107 that are multiples of 4, 7, and 14, we need to identify the least common multiple (LCM) of these numbers. Since 14 is a multiple of 7, we only need to consider the LCM of 4 and 14. The LCM of 4 and 14 is 28. Now, we seek multiples of 28 that are within the specified range.
The first multiple of 28 after 61 is 84, and the second and last one before 107 is 112, which is outside our range. Therefore, given the constraints, the only number Keisha could choose that is a multiple of 4, 7, and 14 between 61 and 107 is 84.
Step-by-step explanation:
To find the numbers that Keisha could choose, we need to find the common multiples of 4, 7, and 14 between 61 and 107.
The multiples of 4 are 4, 8, 12, 16, 20, ...
The multiples of 7 are 7, 14, 21, 28, 35, ...
The multiples of 14 are 14, 28, 42, 56, 70, ...
Looking at the lists, we can see that the common multiples are 28 and 56.
So, Keisha could choose either 28 or 56 as her number