Question

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 ....

Answer 1

(m,n) = (6,60) or (12,30)

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,
`n = (360)/(m)`

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)