Three 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?

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  1. 92 mins
  2. 72 mins 
  3. 32 mins
  4. 82 mins

Answer (Detailed Solution Below)

Option 2 : 72 mins 
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Detailed Solution

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Given:

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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