LCM OF ALGEBRAIC TERMS

Example :

Find the LCM of the following

(i)  x³ y² , xyz 

(ii)  3x²yz, 4x³ y³

(iii)  a²bc, b²ca , c²a b

(iv)  66 a⁴b²c³ , 44 a³b⁴c² , 24 a²b³c⁴

(v)  a^(m+1), a^(m+2), a^(m+3)

(vi)  x²y+xy², x²+xy

(i)  Answer :

x³ y²  =  x ⋅ x ⋅ x ⋅ y ⋅ y

xyz  =  x ⋅ y ⋅ z

Comparing x terms (LCM) is x³

Comparing y terms (LCM) is y²

So, the required LCM is x³ y² z.

(ii)  Answer :

3x²yz, 4x³ y³

3x²yz  =  3 ⋅ x ⋅ x ⋅ y ⋅ z

4x³ y³  =  4 ⋅ x ⋅ x ⋅ x ⋅ y ⋅ y⋅ y

Comparing x terms (LCM) is x³

Comparing y terms (LCM) is y³

So, the required LCM is 12x³ y³z.

(iii)  Answer :

a²bc, b²ca , c²a b

By comparing the given terms, the least common multiple is

a² b²c²

(iv)  Answer :

66 a⁴b²c³, 44 a³b⁴c², 24 a²b³c⁴

66  =  2⋅3⋅11

44  =  2²⋅11

24  =  2³⋅3

Highest common factor of 66, 44 and 24 is 2³ ⋅ 11 ⋅ 3

  =  264

Highest common factor of a⁴b²c³, a³b⁴c² and a²b³c⁴

=  a⁴b⁴c⁴

So, the required LCM is 264a⁴b⁴c⁴.

(v)  Answer :

a^(m+1), a^(m+2), a^(m+3)

a^(m+1)  =  a^m ⋅ a

a^(m+2)  =  a^m ⋅ a²

a^(m+3)  =  a^m ⋅ a³

We find a^m in common for all and highest "a" term is a³.

=  a^m⋅ a³

=  a^(m+3)

So, the required LCM is a^(m+3).

(vi)   Answer :

x²y+xy², x²+xy

x²y+xy²  =  xy(x+y)

x²+xy  =  x(x + y)

By comparing the factors, the least common multiple is 

xy(x+y) 

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