-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

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 \(10\).