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Two numbers have these properties both numbers are greater than 6 their highest common factor is 6 their lowest common multiple is 60 find the two numbers writing your answers on one line in the form the two numbers are ... And ....

Respuesta :

(m,n)  =  (6,60) or  (12,30)  

Step-by-step explanation:

Here, given:

1. Both numbers are greater than 6.

2. The H C F of both numbers  = 6

⇒ Both numbers are multiple of 6

3. The Lowest Common Multiple  = 60

Let us assume the both given numbers are m and n.

Now, as we know : Product of both numbers  =  LCM x HCF

⇒  m n =  60 x 6

or, m n = 360

or, [tex]n = \frac{360}{m}[/tex]

Here, as per the given condition:

(6,60), (12,30),(18,20),(24,15) all the values have a product of 360.

But after checking each pair, we get:

Only, (6,60), (12,30) satisfy the given condition (2) and (3) both.

Hence, any of the pair  (6,60) or  (12,30)   can be the needed answer to the given condition.

or, (m,n)  =   (6,60) or  (12,30)  

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