How many pairs of natural numbers exist whose LCM is 540 and GCD is 18?
Answers
How many common multiple exists for any two natural numbers
Answer:
11 pairs of natural numbers exist whose LCM is 540 and GCD is 18
Step-by-step explanation:
Given that the GCD = HCF = 18
It means that 18 can divide both the numbers.
Therefore, let the numbers be 18x and 18y
We know that product of two numbers = LCM * GCD
=> 18x * 18y = 540 * 18
=> x * y = 540
Now we need to find pairs of x and y which on multiplication gives 540
We know 1 * 540 = 540 , therefore, (1, 540) is a pair
Similarly, other pairs are:
(2, 270) (3, 180), (4, 135), (5, 108), (6, 90), (9,60), (10, 54), (12, 45), (15, 36), (18,30), (20,27)
after this 27 * 12 will also give us 540 and the pair (27, 20) will be formed
But we have already found this pair of number, so we need not rewrite this.
This will continue until we get 1 * 540 = 540
Therefore, total number of pairs of natural numbers are 11.