### Video Transcript

A quarter moon occurs every 15
days. If the last quarter moon occurred
on a Monday, how many days will pass before a quarter moon occurs again on a
Monday?

We are told in the question that a
quarter moon occurs every 15 days. As there are seven days in a week,
a Monday occurs every seven days. In order to calculate how many days
will pass before a quarter moon occurs again on a Monday, we need to find the LCM or
least common multiple of 15 and seven. The LCM is the smallest positive
integer that is a multiple of two or more numbers. We need to consider the seven and
15 times table. After writing the first five
multiples of each of these numbers, there is no common multiple.

We know that 15 multiplied by seven
is 105. This means that 105 is a common
multiple of 15 and seven. This means that the highest number
we will need to write in the 15 times table is 105. Continuing with the multiples of
seven, we notice that none of these are in the 15 times table until we reach
105. The least or lowest common multiple
of seven and 15 is 105. We can therefore conclude that it
will take 105 days before a quarter moon occurs again on a Monday.