Question

The lcm of two numbers .is 45 and their hcf is 5. How many such pairs of numbers are possible

Answer 1

Answer:

the numbers are 5 and 45

Step-by-step explanation:

We should know that,

Product of the 2 numbers = LCM × HCF

(This is mathematically proven)

So, LCM = 45 and HCF = 5

Now, let the numbers be 5a and 5b where a and b are coprimes

(Coprimes means there are no other common factors between a and b)

Now, I said 5a and 5b because, now a and b are coprimes and if we take the HCF of a and b we get

HCF = 1

But we need HCF = 5

so, the numbers are 5a and 5b

so, 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

b = 9

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

So, the possible number is 5(1) and 5(9) = 5 and 45

So the numbers are 5 and 45

Answer 2

Answer:

We should know that,

Product of the 2 numbers = LCM × HCF

(This is mathematically proven)

So, LCM = 45 and HCF = 5

Now, let the numbers be 5a and 5b where a and b are coprimes

(Coprimes means there are no other common factors between a and b)

Now, I said 5a and 5b because, now a and b are coprimes and if we take the HCF of a and b we get

HCF = 1

But we need HCF = 5

so, the numbers are 5a and 5b

so, 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

b = 9

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

So, the possible number is 5(1) and 5(9) = 5 and 45

So, the numbers are 5 and 45

And one and only one pair is possible

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

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