Question

Find the Least Common Multiple of of these two monomials: 16jk^8m^5 and 20j^9k^4m^6
A~ 80j^10k^12m^11
B~ 80j^9k^8m^6
C~ 4jk^4m^5
D~ 36j^9k^8^m^6

Answer 1

\(16jk^8m^5 = 4(4) j k^4 k^4 m^5 = 4 j k^4 m^5 (4 k^4)\)

\(20j^9k^4m^6 = 4 j k^4 m^5 (5 j^8 m) \)

\(\implies gcd(16jk^8m^5, 20j^9k^4m^6) = 4 j k^4 m^5\)

\(lcm( \alpha, \beta) = \dfrac{\alpha \beta}{gcd(\alpha, \beta)} = \dfrac{16jk^8m^5 \cdot 20j^9k^4m^6 }{4 j k^4 m^5} = 80j^9k^8m^6 \)