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March 25, 2017

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Find the least common multiple of the monomials. 5a squared, and 16a cubed. Also 17b squared and 3b cubed. Could you show me how to do these.
Thank you,
Sandy

  • algebra - ,

    5a^2 = 5*a^2
    16a^2 = 2^4 * a^2

    take the highest power of each prime (assuming a is not divisible by 2 or 5)

    LCM = 2^4*5*a^2 = 80a^2

    17b^2 = 17*b^2
    3b^3 = 3*b^3

    LCM = 3*17*b^3 = 51b^3

    The LCM is the smallest number that can be divided by each of the two given numbers.

    another example: LCM(20,30,50,80):

    20 = 2^2 * 5
    30 = 2 * 3 * 5
    50 = 2 * 5^2
    80 = 2^4 * 5

    LCM = 2^4 * 3 * 5^2 = 1200

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