Question

is it possible to have a pair of numbers whose HCF is 12 and LCM is 220.

answer step by step and fast please​

Answer 1

Answer:

It is not possible, with reference to whole numbers. (It can only be possible with real numbers)

Step-by-step explanation:

We need two numbers which HCF = 12 and LCM = 220

Now,

Let 'a' and 'b' be 2 numbers who are coprimes.

Coprime numbers are numbers who do not have a common factor except 1, or in simple words their HCF will be 1

Now,

Let the numbers be 12a and 12b

You might think, why I took 12a and 12b instead of just 'a' and 'b'.

Remember that, a and b are coprimes, so their HCF will be 1, when it is 12a and 12b, their HCF will be 12

Now, we know that,

Product of numbers = HCF × LCM

So,

12a × 12b = 12 × 220

144ab = 2640

ab = 2640/144

ab = 55/3

Now, if they are possible, then the 2 numbers must be whole numbers, but we have got fractions, this shows that it is not possible to have two whole numbers whose HCF = 12 and LCM = 220, but it doesn't mean it is not possible with all the numbers in the number system.

Well, there exists a lot real numbers which make this possible, but here we are only considering whole numbers, so it is not possible.

Hope it helped and believing you understood it........All the best