Find the LCM of the following

66a⁴b²c³, 44a³b⁴c², 24a²b³c⁴

Given terms: –

66a⁴b²c³, 44a³b⁴c², 24a²b³c⁴

Formula used: –

LCM = Least Common Multiple

Means it is the lowest term by which every element must be

divided completely;

66a⁴b²c³ = 3 × 2 × 11 × a × a × a × a × b × b × c × c × c

44a³b⁴c² = 2 × 2 × 11 × a × a × a × b × b × b × b × c × c

24a²b³c⁴ = 2 × 2 × 2 × 3 × a × a × b × b × b × c × c × c × c

⇒ first find the common factors in all terms

Common factor in all terms = 2 × a × a × b × b × c × c

Common factors from any 2 terms

2a²b²c² × [(3 × 11 × a × a × c)( 2 × 11 × a × b × b)( 2 × 2 × 3 × b × c × c)]

2a²b²c² × (3 × 11 × 2 × a × b × c)[(a)(b)(2c)]

⇒ then multiply the remaining factors of terms in common

factor to get the LCM

= 2a²b²c² × (66abc) × (2abc)

(66 × 2 × 2)( a²b²c² × abc × abc )

264 a⁴b⁴c⁴

Conclusion: –

The LCM of given terms [66a⁴b²c³, 44a³b⁴c², 24a²b³c⁴] is 264 a⁴b⁴c⁴