Question

Two numbers have these properties both numbers are greater than 6 their highst common factor is 6 there lowest common factor is 60 find the two numbers,writing your answers on one line in the form

Answer 1

Answer:

The two numbers are 12 and 30

Step-by-step explanation:

Both numbers are greater than 6

Their HCF is 6 and their LCM is 60.

A possible guess of the two numbers will be 6 and 60, which were given in the question, because they satisfy this HCF and LCM values, but the question also tells us that both numbers are greater than 6.

Now, we will obtain the answer using what we have.

Since the HCF is 6, that means that both numbers that we seek are a multiple of 6.

Next, the LCM is 60. We can divide the LCM by the HCF, that is $\frac{60}{6}$ = 10

This tells us that the two numbers are within 6 and (6 × 10).

Next we write out the factors of the 10 that we got by dividing the LCM by the HCF.

Factors of 10 are: 1, 2, 5 and 10.

We multiply each of this by 6 (which is the HCF, recall that we had said that HCF means that the numbers are a multiple of 6), to get the numbers; 6, 12, 30 and 60

Since 6 and 60 are already the given LCM and HCF, the two numbers that we seek are 12 and 30.