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    Three bells ring at intervals of 12 minutes, 18 minutes, and 24 minutes,respectively. If they all ring together at 12:00 p.m., In how many minuteswill
    Question

    Three bells ring at intervals of 12 minutes, 18 minutes, and 24 minutes,respectively. If they all ring together at 12:00 p.m., In how many minuteswill they all ring together again?

    A.

    108

    B.

    6

    C.

    72

    D.

    36

    Correct option is C

    ​Given:

    The intervals at which the bells ring are 12 minutes, 18 minutes, and 24 minutes

    Solution:

      Prime factorization

      12 = 22×32^2 \times 3​​

      18 =2×32 2 \times 3^2​​

      24 = 23×32^3 \times 3​​

      LCM(12,18,24) = 23×32=8×92^3 \times 3^2 = 8 \times 9​ = 72

      So,

      Thus, the bells will all ring together again after 72 minutes.

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