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Secondary I • 1yr.

My teacher tells me that to work on fractions, it is useful to master LCM. How can I find it? I have heard of multiples and trees.

Mathematics
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Explanations (1)

  • Explanation from Alloprof

    Explanation from Alloprof

    This Explanation was submitted by a member of the Alloprof team.

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    Team Alloprof • 1yr.

    Good evening,

    The multiples method and the factor tree method are indeed used to find the LCM! There is a third technique, the table, but let's tackle the ones you mentioned! 

    1. Method of multiples.

    To find the LCM, we first make a list of the multiples of each number.

    Suppose the numbers 6, 9 and 12. 

    The multiples of 6 = {6, 12, 18, 24, 30, 36, 42, 48,…}

    The multiples of 9 = {9, 18, 27, 36, 45, 54 , 63, 72,…}

    The multiples of 12 = {12, 24, 36, 48, 60, 72, 84, 96,…}

    We observe that 36 is the lowest common multiple!

    2. Factor tree method.

    Find the LCM of two numbers:

    We decompose the two numbers using a factor tree until we get only prime factors. Common factors and unique factors are identified. 

    Example 9 and 12.

    Capture d’écran (1152).png


    We get 9 = 3 x 3.

    We get 12 = 2 x 2 x 3.

    The common factor (in orange) is 3.

    The unique factors (in blue) are 3, 2 and 2.

    The common factors are multiplied by the single factors.

    So 3 x 3 x 2 x 2 = 36 which is the LCM.