Question

Can 72 and 20 respectively be the LCM and HCF of two ‘numbers’? Give a reason.

Answer 1

Hint: For solving this question you should know about the least common multiple of any numbers. We will first find factors of given numbers and then we will take those factors which are not common in the factors of the three numbers given and if two factors in the factors of given three numbers are the same then we will take it once only. Hence, we will determine the least common multiple (LCM) of given numbers.

Complete step by step answer:
For calculating the greatest common factor or GCF we will do factors of the given digits and then we will take the all common values. And see the greatest common value in this.
According to the question, 72 and 20 are the LCM and HCF of two ‘numbers’.
The LCM refers to the least common multiple or we can also use it as the least common divisor (L.C.D.). If we assume that the least common multiple of two numbers ‘a’ and ‘b’, then the LCM will be the least positive number which is evenly divisible or is a multiple of both ‘a’ and ‘b’.
For the greatest common factor
We can solve this by the factorization method. In this method we make factors of all digits which are given and then take the common digits outside and then we see the greatest common value in this.
So, 72 and 20 cannot be the LCM and HCF of two numbers because it is the condition that HCF must be divisible completely by LCM. But in this case when we divide 72 by 20, then
\[20\overline{\left){\begin{align}
  & 72 \\
 & \underline{60} \\
 & \underline{12} \\
\end{align}}\right.}\left| \!{\underline {\,
  3 \,}} \right. \]
Here, 12 is the remainder. So, it can’t possible to be LCM and HCF of two numbers.

Note: While solving these types of questions you have to mind that if there are any remainder after dividing the LCM by HCF, then it can’t be the LCM and HCF of two numbers. The LCM of the numbers may seem easy to find but one additional factor or one less factor if taken may result in the entire question going wrong. Also do not confuse LCM with HCF. Because both are different terms.