Question

If 19 and 1140 are the respective hcf and lcm of two numbers, which are greater than 19 then what will be the possible number of such pair?

Answer 1

Heyy mate ❤✌✌❤

Here's your Answer.....

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Let the two number be a and b.

A × b = 19 × 1140

Since, HCF = 19..

Therefore,

19a × 19b = 19 × 1140

=> a×b = 60.

So, the possible pairs are (1,60)(2,30)(3,20),(4,15),(5,12),(6,10)..

Total 6 pairs.
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Answer 2

Product of HCF and LCM = product of the numbers
Then, product of the numbers = 19 x 1140
Let 19a and 19b be the numbers.
19a x 19b = 19 x 1140
ab = 19 x 1140 / 19 x 19 = 60

If ab = 60 then (a,b) = (1,60), (2,30), (3,20), (4,15), (5,12) and (6,10).
Since a and b are co-primes then (a,b) = (1,60), (4,15) and (5,12)
Hence the number of such pairs = 3