Q. 4 K4.0( 4 Votes )

# Let’s find the L.C.M. of the following algebraic expressions:

3a^{2}-5ab-12b^{2}, a^{5}-27a^{2}b^{3}, 9a^{2} + 24ab + 16b^{2}

Answer :

factors of 3a^{2}-5ab-12b^{2}

=3a^{2}-9ab + 4ab-12b^{2}

=3a(a-3b) + 4b(a-3b)

=(3a + 4b)(a-3b)

Factors of a^{5}-27a^{2}b^{3}

=a^{2}(a^{3}-27b^{3})

=a^{2}(a-3b)(a^{2} + 3ab + 9b^{2})

Factors of 9a^{2} + 24ab + 16b^{2}

=9a^{2} + 12ab + 12ab + 16b^{2}

=3a(3a + 4b) + 4b(3a + 4b)

=(3a + 4b)^{2}

LCM is the lowest common multiple, which is the product of all the common factors taken once and the remaining factors as it is.

∴ the LCM of 3a^{2}-5ab-12b^{2}, a^{5}-27a^{2}b^{3}, 9a^{2} + 24ab + 16b^{2}is

a^{2}(a-3b)(a^{2} + 3ab + 9b^{2}) (3a + 4b)^{2}

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