Video: Solving Word Problems Involving the Lowest Common Multiple

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

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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.

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