-Ready Least Common Multiple - Instruction - Level F To train for a race, Nathan bikes every 2 days and swims every 5 days. He biked on October 2 and he swam on October 5

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To solve the problem, we need to determine on what day Nathan will both bike and swim.

1. Nathan bikes every $$2$$ days and he started on October 2. Thus, his biking days are:
   $$
   \text{October }2,\, 4,\, 6,\, 8,\, 10,\, \ldots
   $$

2. Nathan swims every $$5$$ days and he started on October 5. Thus, his swimming days are:
   $$
   \text{October }5,\, 10,\, 15,\, 20,\, \ldots
   $$

3. We observe that October 10 appears in both schedules.

4. Alternatively, we can find the least common multiple (LCM) of the intervals $$2$$ and $$5$$. Since:
   $$
   \text{LCM}(2,5) = 10,
   $$
   and considering the offsets of the starting days, the common training day will be $$10$$ days after the later starting day. Since swimming started on October 5, the next simultaneous event occurs on October:
   $$
   5+5=10 \quad \text{(October 10)}.
   $$

Thus, the next day Nathan bikes and swims on the same day is October $$10$$.
Nathan will bike and swim on October 10.

-Ready Least Common Multiple - Instruction - Level F To train for a race, Nathan bikes every 2 days and swims every 5 days. He biked on October 2 and he swam on October 5

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