Question

the product of two numbers is 2 power 15* 3 power 12* 5 power 19. If their HCF is 2 power 4* 3 power 5* 5 power 6 then find their LCM.​

Answer 1

Given:

• Product of 2 numbers = 2¹⁵ × 3¹² × 5¹⁹

• HCF = 2⁴ × 3⁵ × 5⁶

To find:

1. LCM = ?

Method:

Use this formula:

HCF × LCM = Product of 2 numbers.

→ 2⁴ × 3⁵ × 5⁶ × LCM = 2¹⁵ × 3¹² × 5¹⁹

$\implies \sf{LCM = \dfrac{2^{15} \times 3^{12} \times 5^{19} }{2^{4} \times 3^{5} \times 5^{6}}}\\\\\\\\\implies \sf{LCM = \dfrac{2^{15}}{2^{4}} \times \dfrac{3^{12} }{3^{5}} \times \dfrac{5^{19} }{5^{6} }}\\\\\\\\\implies \sf{LCM = 2^{(15-4)} \times 3^{(12-5)} \times 5^{(19-6)}}\\\\\\\implies \large{\bf{\boxed{\bf{LCM = 2^{11} \times 3^{7} \times 5^{13}}}}}$

$\bf{\large{Main \: Concept \: used:}}\\\\\sf{\dfrac{a^{m} }{a^{n} } = a^{(m-n)} }$