Q. 4 J4.0( 8 Votes )

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

(a^{2} + 2a)2 , 2a^{3} + 3a^{2}-2a, 2a^{4}-3a^{3}-12a^{2}

Answer :

factors of (a^{2} + 2a)^{2}

= a^{4} + 4a^{2} + 4a^{3}

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

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

= a^{2}(a(a + 2) + 2(a + 2))

= a^{2}(a + 2)(a + 2)

= a^{2}(a + 2)^{2}

Factors of 2a^{3} + 3a^{2}-2a

=a(2a^{2} + 3a-2)

=a(2a^{2} + 4a-a-2)

=a{2a(a + 2)-1(a + 2)}

=a(a + 2) (2a-1)

Factors of 2a^{4}-3a^{3}-14a^{2}

=a^{2}(2a^{2}-3a-14)

=a^{2}(2a^{2} + 4a-7a-14)

= a^{2}(2a(a + 2)-7(a + 2))

= a^{2}(2a-7) (a + 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 (a^{2} + 2a)2, 2a^{3} + 3a^{2}-2a, 2a^{4}-3a^{3}-12a^{2} is a^{2}(a + 2)^{2}(2a-1)(2a-7).

Rate this question :

Let's find L.C.M. of 4a^{2}b^{4}c, 12a^{3}bc^{5} and 18a^{2}b^{3}c^{2}

Let's find the L.C.M. of 2(x – 4) and (x^{2} – 3x + 2)

Let’s solve the equations below:

West Bengal - Mathematics

Let’s solve the equations below:

5x = 30

West Bengal - Mathematics

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

11a^{2}bc^{2}, 33a^{2}b^{2}c, 55a^{2}bc^{2}

West Bengal - Mathematics

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

5a^{5}b, 15ab^{2}c, 25a^{2}b^{2}c^{2}

West Bengal - Mathematics

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

7p^{2}q^{3}, 35p^{3}q, 42pq^{4}

West Bengal - Mathematics

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

2x^{2}y^{3}, 10x^{3}y

West Bengal - Mathematics

Let’s solve the equations below:

West Bengal - Mathematics

Let’s solve the equations below:

West Bengal - Mathematics