Answer
Every $140$ days
Work Step by Step
To determine how often Elizabeth Kaster and Lori Sypher are in New Orleans on the same day, we need to find the least common multiple ($LCM$) of $35$ and $20$. The $LCM$ will represent the number of days after which their schedules will align.
To find the $LCM$ of $35$ and $20$, we calculate their prime factorizations:
$35 = 5 \cdot 7$
$20 = 2\cdot 2\cdot 5$
To calculate the $LCM$, we take the highest power of each prime factor:
$LCM(35, 20) = 2\cdot 2 \cdot 5 \cdot 7 = 140$.
Thus, Elizabeth and Lori will be in New Orleans on the same day every $140$ days.
