L.C.M OF ALGEBRAIC EXPRESSIONS

           Examples

Find the l.c.m of the following:

          1.     2a2 and 6ab2

                 Solution

Index Method

2a2 = 2 x a2

6ab2 = 2 x 3 x a x b2

As usual, we pick all the bases present. If a base is common to the two expressions, pock the one with the higher power.

Lcm = 2 x 3 x a2 x b2

Lcm = 6a2b2

Table method

2 2a2 6ab2
3 a2 3ab2
a a2 ab2
a a b2
b 1 b2
b 1 b
  1 1

L.C.M = 2 x 3 x a x a x b x b

Lcm = 6 x a2 x b2

Lcm = 6a2b2

       

2.       Find the lcm of 6 α 2 β, 8 α 3β 2 and 18 α β

                Solution

Index Method

6 α 2 β = 2 x 3 x α 2 x β

8 α 3β 2 = 23   x α 3 x β 2

18 α β = 2 x 32 x α x β

Lcm = 23 x 32 x α 3 x β 2

Lcm = 8 x 9 x α 3 x β 2

Lcm = 72α 3β 2

Note: every base must be selected. When a base is common to two or more expressions, select the one with the highest power.

Table method

 

2 6 α 2 β 8 α 3β 2 18 α β
2 3 α 2 β 4 α 3β 2 9 α β
2 3 α 2 β 2 α 3β 2 9 α β
3 3 α 2 β α 3β 2 9 α β
3 α 2 β α 3β 2 3 α β
α α 2 β α 3β 2 α β
α α β α 2 β 2 β
α β α β 2 β
β β β 2 β
β 1 β 1
  1 1 1

 

lcm = 2 x 2 x 2 x 3 x 3 x α x α x α x β x β

Lcm = 23 x 32 x α 3 x β 2

Lcm = 8 x 9 x α 3 x β 2

Lcm = 72α 3β 2

 

           Exercise I

Find the lcm of the following expressions

        1.    4a and 6b

        2.    12j2 and 18jk

        3.    6, 4u and 5u

        4.    6x2y, 4xy and 9xy3

        5.    15p2q3, 20pq2 and 12p3q

        6.    6ab2c and 8a2bc3

        7.    9s3t, 11su and 3st2u

        8.    25mn2, 15m2n4, 20mn and 5m

        9.    3x, 2t, 5j3 and 4y2

       10.    27p, 6p2 and 3

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