Find the LCM of the following
(x + 4)2 (x – 3)3, (x – 1)(x + 4)(x – 3)2
Given terms: –
(x + 4)2 (x – 3)3, (x – 1)(x + 4)(x – 3)2
Formula used: –
LCM = Least Common Multiple
Means it is the lowest term by which every element must be divided completely;
(x + 4)2 (x – 3)3 = (x + 4) × (x + 4) × (x – 3) × (x – 3) × (x – 3)
(x – 1)(x + 4)(x – 3)2 = (x – 1) × (x + 4) × (x – 3) × (x – 3)
⇒ first find the common factors in all terms
Common factor = (x + 4) × (x – 3) × (x – 3)
⇒ then multiply the remaining factors of terms in common
factor to get the LCM
= (x + 4)(x – 3)(x – 3) × [(x + 4) × (x – 3) × (x – 1)]
= (x + 4)2 (x – 3)3(x – 1)
Conclusion: –
The LCM of given terms [(x + 4)2 (x – 3)3, (x – 1)(x + 4)(x – 3)2] is
(x + 4)2 (x – 3)3(x – 1)
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