



 
Kiyah, The route 1 bus will stop at the gym in 12 minutes, 24 minutes, 36 minutes and so on. Every stop time is a multiple of 12. The route 2 bus will stop in 15 minutes, 30 minutes etc. Every stop time is a multiple of 15. You can just continue each list of times and look for the first time the same number appears in both lists. So you are looking for a common multiple of 12 and 15, in fact the smallest or least number that is a multiple of 12 and 15. We call the number you are looking for the least common multiple or LCM of 12 and 15. The listing method can become tedious. There is another technique that depends on the prime factorization of the numbers.
From this we can see that
Hence if number is a multiple of 12 and 15 its prime factorization must contain at least two 2s, at least one 3 and at least one 5. What is the smallest such number? Penny  


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