Question

Product of HCF and LCM of smallest prime number and smallest composite number is what?

Answer 1

Hint: To solve this question, we will first of all determine what is the smallest prime number and smallest composite number. Then we will proceed to finding HCF and LCM of them. And then go for their product.

Complete step by step answer:
We have the Smallest prime number as 2 and the smallest composite number = 4
Let a be 2, the smallest prime number and b be 4, the smallest composite number.
We have to find the HCF and LCM of a and b.
For this we will write the multiples of a and b which is given as,
2 = 2x1.
And 4 = 2x2.

Then LCM of a=2 and b=4 is 4.

And the HCF of a=2 and b=4 is 2.

Therefore, product of LCM and HCF = 4 × 2

Hence, we get the product of LCM and HCF AS 8.

There is one more way to solve such a type of question.
We have a formula given as,
\[HCF(a,b).LCM(a,b)=a.b\]
Therefore, using the above formula, we have that the product of hcf and lcm of two numbers can also be given as the product of the two numbers.
Hence, we get the product of the Smallest prime number as 2 and the smallest composite number as 4 is given by
4 × 2 = 8, which is the required result.

Note:
The possibility of error in such a type of question can be directly putting the formula given as \[HCF(a,b).LCM(a,b)=a.b\] and solving the question. This formula holds true when we only have to find the product of HCF and LCM of only two numbers and not more than two. Always opt for going through the long process to get the desired result.