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GCD of Polynomials

State whether...

Question

State whether True or False.
The H.C.F. and L.C.M. of:

$a^{2} + 3 a, a^{2} + 4 a + 3$ and $a^{2} + 3 a + 2$ is $1; a (a + 3) (a + 1) (a + 2)$
If true then enter $1$ and if false then enter $0$

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Solution

Factorizing $a^{2} + 3 a, a^{2} + 4 a + 3$ and $a^{2} + 3 a + 2,$
$a^{2} + 3 a = a (a + 3)$
$a^{2} + 4 a + 3 = (a + 3) (a + 1)$
$a^{2} + 3 a + 2 = (a + 1) (a + 2)$
H.C.F. $= 1$
L.C.M. $= a (a + 3) (a + 1) (a + 2)$

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