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Find the LCM of 5, 3m, and 20.

Mathematics

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Answer

60m\text{60m}

Step-by-step solution

3 steps
  1. Identify the numbers and terms.

    The given terms are ୫ (5), $3m$, and ୨୦ (20). The question asks for the ଲ.ସା.ଗୁ. (L.C.M.), which stands for Least Common Multiple.

  2. Find the LCM of the numerical coefficients.

    The numerical coefficients are 5, 3, and 20.
    Prime factorization of each number:
    5=515 = 5^1
    3=313 = 3^1
    20=22×5120 = 2^2 \times 5^1

    To find the LCM, we take the highest power of all prime factors present:
    LCM(5,3,20)=22×31×51=4×3×5=60\text{LCM}(5, 3, 20) = 2^2 \times 3^1 \times 5^1 = 4 \times 3 \times 5 = 60.

  3. Include the variable part.

    The variable present in the terms is mm.
    Therefore, the LCM of 5, 3m3m, and 20 is the numerical LCM multiplied by the variable.

    The LCM is 60m60m.

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