Every three years, Huntington School hosts the state gymnastics competition. Every seven years, it hosts the state mathematics competition. If the last time the school hosted both events in the same year was 2003, in what year will the school host both events in the same year again?
We are told that the school hosts the gymnastics competition every three years. It hosts the math competition every seven years. In order to work out when the school will host both events in the same year, we need to find the least common multiple, or LCM, of three and seven. The LCM of three and seven is the smallest positive integer that is a multiple of both three and seven.
We can begin by writing the numbers in the three times table, the multiples of three. They are three, six, nine, 12, and so on. The multiples of seven are seven, 14, 21, 28, 35, and so on. We can see from these lists that the smallest positive integer that is a multiple of three and seven is 21. Therefore, the LCM of three and seven is 21.
This means that Huntington School will host both events every 21 years. As they last hosted both events in 2003, they will next host both events in 2024, as 2003 plus 21 is 2024.