To find: the othermonomial. Given: the GCF of 12x2y3 and another monomial is 6xy3, and their LCM is 36x2y4.

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To find: the othermonomial.  Given: the GCF of 12x2y3 and another monomial is 6xy3, and their LCM is 36x2y4.

Clara Reese · Accepted Answer

Calculation:  As per problem,  Compare the coefficients,  The GCF of 12 and the other number is 6, so the number is a multiple of 6  Their LCM is 36, so the number is factor of 36  The multiples of 6 which are also factors of 36 are 6,12,18 and 36  Now, LCM and GCF of 12 and 6 is 6, so the number is not 6  And, the LCM and GCF of 12 and 12 is 12, so the number is not 12  However, LCM and GCF of 12 and 18 is  12=2⋅6  18=3⋅6  LCM=2⋅3⋅6=36  Therefore, the coefficient of the monomial is 18.  The first monomial has x2 as variable, and the GCF has x, so the other monomial has x.  The first monomial has y3 as variable, but the LCM has y4, so the other monomial has y4.  Hence, the other monomial is 18xy4

To find: the othermonomial. Given: the GCF of 12x^{2}y^{3} and another

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