KnowledgeBoat Logo
|

Mathematics

Can two numbers have 15 as their HCF and 110 as their LCM? Give reason to justify your answer.

Number Play

3 Likes

Answer

We know that the LCM of two numbers is always exactly divisible by their HCF.

On dividing 110 by 15:

x21715)110‾x(−105‾x2+25\begin{array}{l} \phantom{x^2 1}{\quad 7} \ 15\overline{\smash{\big)}110} \ \phantom{x^(}\phantom{}\underline{-105} \ \phantom{{x^2 } + 2 } 5 \ \end{array}

We get quotient = 7 and remainder = 5.

Since the remainder ≠ 0, 110 is not exactly divisible by 15.

Hence, two numbers cannot have 15 as their H.C.F. and 110 as their L.C.M. and L.C.M. of two numbers is always exactly divisible by H.C.F.

Answered By

2 Likes

Related Questions