Question
Download Solution PDFThree friends are exercising together. The first friend runs a lap in 12 minutes, the second in 18 minutes, and the third in 24 minutes. If they all start running together, after how many minutes will they all finish a lap together again?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The first friend runs a lap in 12 minutes,
The second friend runs a lap in 18 minutes,
The third friend runs a lap in 24 minutes.
Formula used:
To find when they will finish together again, we need to calculate the Least Common Multiple (LCM) of their times.
Calculation:
LCM of 12, 18, and 24:
Prime factorization of 12 = 2² × 3
Prime factorization of 18 = 2 × 3²
Prime factorization of 24 = 2³ × 3
LCM is found by taking the highest powers of all prime factors:
LCM = 2³ × 3² = 8 × 9 = 72
∴ They will all finish a lap together again after 72 minutes.
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