Question

The product of HCF and LCM of two number is 620.If one of the numbers is 20, what is the other number.

Answer 1

LCM or Least common multiple is the Least number which is exactly divisible by two or more numbers. HCF or Highest common factor is the Highest factor present between two numbers.

$\begin{gathered}\boxed{\begin{array}{c}\textbf{\dag \ \underline{\:Result on HCF and LCM of two numbers\:}}\\\\ (1) \: \rm{HCF \times LCM = product \: of \: the \: two \: given \: numbers.}\\ \\ \textrm{(2) HCF divides LCM completely.}\end{array}}\end{gathered}$

In the above question, products of HCF and and LCM has been given as well as with one of the number and we've been asked to find the value of other number.

So, let's suppose that, xx be the other number. And we know that, the product of LCM and HCF is equal to the product of other numbers. Therefore,

$\begin{gathered}\implies 620 = 20 \times x \\ \\ \implies 620 = 20x \\ \\ \implies x = \cancel{\dfrac{620}{20}} \\ \\ \implies \boxed{x = 31}\end{gathered}$

Hence, the other required number is 31.

Answer 2

Given:

The product of HCF and LCM of two numbers is $620$.

One number$=20$

To find: the other number.

Solution:

Apply,

$\[LCM \times HCF = 1st\,\,number{\rm{ }} \times {\rm{2}}nd{\rm{ }}number\]$

$\[\begin{array}{l} \Rightarrow {\rm{620 = 20}} \times {\rm{2}}nd{\rm{ }}number\\ \Rightarrow {\rm{2}}nd{\rm{ }}number = \frac{{620}}{{20}}\\ \Rightarrow {\rm{2}}nd{\rm{ }}number = 31\end{array}\]$

Therefore, the other number is $31.$