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18 December, 07:49

Find the GCF and LCM of 217x328x11 and 213x345x74and explain your reasoning.

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  1. 18 December, 10:28
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    Given expressions are,

    217 x 328 x 11

    213 x 345 x 74,

    Since, 217 = 7 * 31

    328 = 2 * 2 * 2 * 41,

    11 = 1 * 11,

    So, we can write, 217 x 328 x 11 = 7 * 31 * 2 * 2 * 2 * 41 * 1 * 11

    Now, 213 = 3 * 71

    345 = 3 * 5 * 23,

    74 = 2 * 37,

    So, 213 x 345 x 74 = 3 * 71 * 3 * 5 * 23 * 3 * 5 * 23

    Thus, GCF (greatest common factor) of the given expressions = 1 (because there are no common factors)

    We know that if two numbers have GCF 1 then their LCM is obtained by multiplying them,

    Hence, LCM (least common multiple) of the given expressions = 217 x 328 x 11 x 213 x 345 x 74
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