Question

the LCM of two numbers is 45 and their HCF IS 5
How many such points of number's are possible ​

Answer 1

Answer:

Number is 5 and 45 for 5a and 5b respectively.

Step-by-step explanation:

According to question,

We know that

Product of two number = L.C.M. of that two number × H.C.F. of that number

So, We see that it is mathematically proven

Let a and b is two number

Now, let the number be 5a and 5b where a and b is corine number.

(corine mean there are no other common factors between a and b)

Now I said that 5a and 5b because, now a and b are copime and if we take the H.C.F. of a and b we get

HCF = 1

But we need HCF = 5

so, number are 5a and 5b

so, putting in formula

5a × 5b = 45 × 5

25ab = 225

ab =225/25 =9

ab = 9

Now the coprimes pairs which satisfy ab = 9 is (1, 9)

where a = 1 and b = 9

See we can't take (3,3) because they have a common factor of 3, we said that a and bare coprimes.

So possible number is 5(1) and 5(9) is 5 and 45 respectively.

Thankyou,

I hope it was helpful to you.

Answered by,

Aaditya Singh