1 Gavin goes to the gym every day, Leeroy every 2 days, Stacey every 3 days,
Jimmy every 4 days, Neil every 5 days, and Tim every 6 days. Today, they are
all at the gym together. How many days later will they next be there together?
E. 90 days

Ask by Lane Patel. in Australia

Mar 28,2025

Question

1 Gavin goes to the gym every day, Leeroy every 2 days, Stacey every 3 days,
Jimmy every 4 days, Neil every 5 days, and Tim every 6 days. Today, they are
all at the gym together. How many days later will they next be there together?
E. 90 days

Ask by Lane Patel. in Australia

Mar 28,2025

UpStudy AI · Accepted Answer

1. We need to find the smallest number of days after which all their schedules coincide. This requires computing the least common multiple (LCM) of their visit cycles:
   
   - Gavin: every $$ 1 $$ day
   - Leeroy: every $$ 2 $$ days
   - Stacey: every $$ 3 $$ days
   - Jimmy: every $$ 4 $$ days
   - Neil: every $$ 5 $$ days
   - Tim: every $$ 6 $$ days

2. First, write the prime factorization for each cycle:
   
   - $$ 1 $$ (no prime factors)
   - $$ 2 = 2 $$
   - $$ 3 = 3 $$
   - $$ 4 = 2^2 $$
   - $$ 5 = 5 $$
   - $$ 6 = 2 \times 3 $$

3. The LCM is found by taking the highest power of each prime that appears:
   
   - For $$ 2 $$: the highest power is $$ 2^2 $$ (from $$ 4 $$).
   - For $$ 3 $$: the highest power is $$ 3 $$ (from $$ 3 $$ or $$ 6 $$).
   - For $$ 5 $$: the highest power is $$ 5 $$.

4. Multiply these together to obtain the LCM:
   
   $$
   \text{LCM} = 2^2 \times 3 \times 5 = 4 \times 3 \times 5 = 60
   $$

5. Therefore, all of them will next be at the gym together in $$ 60 $$ days.

So, the correct answer is option D: $$ 60 $$ days.
They will next be at the gym together in 60 days.

1 Gavin goes to the gym every day, Leeroy every 2 days, Stacey every 3 days,
Jimmy every 4 days, Neil every 5 days, and Tim every 6 days. Today, they are
all at the gym together. How many days later will they next be there together?
E. 90 days

Upstudy AI Solution

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Solution

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1 Gavin goes to the gym every day, Leeroy every 2 days, Stacey every 3 days, Jimmy every 4 days, Neil every 5 days, and Tim every 6 days. Today, they are all at the gym together. How many days later will they next be there together? E. 90 days

Upstudy AI Solution

Answer

Solution

Bonus Knowledge

Related Questions

Latest Arithmetic Questions

1 Gavin goes to the gym every day, Leeroy every 2 days, Stacey every 3 days,
Jimmy every 4 days, Neil every 5 days, and Tim every 6 days. Today, they are
all at the gym together. How many days later will they next be there together?
E. 90 days