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Find the L.C.M. of the following numbers below: a) 20 and 9 b) 6 and 3

Mathematics

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Answers

2 parts
a

180\text{180}

b

6\text{6}

Step-by-step solution

6 steps

Part a· 3 steps

Find the L.C.M. of 20 and 9.

  1. Find the prime factorization of each number.

    20=2×2×5=22×5120 = 2 \times 2 \times 5 = 2^2 \times 5^1 9=3×3=329 = 3 \times 3 = 3^2

  2. Identify all prime factors and take the highest power of each.

    The prime factors are 2, 3, and 5.
    The highest power of 2 is 222^2.
    The highest power of 3 is 323^2.
    The highest power of 5 is 515^1.

  3. Multiply these highest powers together to find the L.C.M.

    L.C.M.(20,9)=22×32×51=4×9×5=36×5=180\text{L.C.M.}(20, 9) = 2^2 \times 3^2 \times 5^1 = 4 \times 9 \times 5 = 36 \times 5 = 180

    The L.C.M. of 20 and 9 is 180\boxed{\text{180}}.

Part b

6\text{6}

Find the L.C.M. of 6 and 3.

  1. Find the prime factorization of each number.

    6=2×3=21×316 = 2 \times 3 = 2^1 \times 3^1 3=313 = 3^1

  2. Identify all prime factors and take the highest power of each.

    The prime factors are 2 and 3.
    The highest power of 2 is 212^1.
    The highest power of 3 is 313^1.

  3. Multiply these highest powers together to find the L.C.M.

    L.C.M.(6,3)=21×31=2×3=6\text{L.C.M.}(6, 3) = 2^1 \times 3^1 = 2 \times 3 = 6

    The L.C.M. of 6 and 3 is 6\boxed{\text{6}}.

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