Troy mows every 3 days and Walter mows every 5 days. How many days will pass before they both mow on the same day?

Troy mows every 3 days and Walter mows every 5 days. How many days will pass before they both mow on the same day?

• A. Least Common Multiple
• B. Greatest Common Divisor
• C. Prime Factorization
• D. Exponent Rules

Answer: (A)

The idea is to find when two repeating schedules line up. Troy mows every 3 days and Walter every 5 days, so the day they both mow is the first day that is a multiple of both 3 and 5. The multiples of 3 are 3, 6, 9, 12, 15, … and the multiples of 5 are 5, 10, 15, …; the earliest common day is 15. Since 3 and 5 have no common factors other than 1, their least common multiple is 3 × 5 = 15, so they’ll both mow again after 15 days. The other options describe different ideas (greatest common divisor, prime factorization, exponent rules) that don’t answer when the schedules align.

The idea is to find when two repeating schedules line up. Troy mows every 3 days and Walter every 5 days, so the day they both mow is the first day that is a multiple of both 3 and 5. The multiples of 3 are 3, 6, 9, 12, 15, … and the multiples of 5 are 5, 10, 15, …; the earliest common day is 15. Since 3 and 5 have no common factors other than 1, their least common multiple is 3 × 5 = 15, so they’ll both mow again after 15 days. The other options describe different ideas (greatest common divisor, prime factorization, exponent rules) that don’t answer when the schedules align.