Trent goes hiking every 9 days and swimming every 6 days. He did both kinds of exercise today. How many days from now will he next go both hiking and swimming again?
Question
Trent goes hiking every 9 days and swimming every 6 days. He did both kinds of exercise today. How many days from now will he next go both hiking and swimming again?
Solution
To solve this problem, we need to find the least common multiple (LCM) of 9 and 6. The LCM of two numbers is the smallest number that is a multiple of both numbers.
Here are the steps:
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List the multiples of each number:
Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, 153, 162, 171, 180...
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120...
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Find the smallest number that appears in both lists:
The smallest number that is a multiple of both 9 and 6 is 18.
So, Trent will next go both hiking and swimming again 18 days from now.
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