Originally Posted by

**bruxism** When you hit a problem like this, try writing down what you know about each number. You know that

A = 2 x ? = 3 x ?

B = 2 X ? = 4 x ?

C = 4 x ? = 3 x ?

Ok so we know that ABC must satisfy these things. A B and C all have factors of either 2 or 4. This means they are all even. That's another clue for you. A also has a factor of 3.

All possible A's must be even and be multiples of 3.

A could be 6, 12, 18, 24 etc.

Now you can test A=6 and see if the other two are satisfied for this A.

Now C must have a HCF with A of 3 and must also be a multiple of 4. 12 satisfies both of these conditions.

A = 6

C = 12

Now b's highest common factor with A is 2, and with C is 4. B = 8 satisfies these conditions.

So

A=6

b=8

c=12

Listing all factors and highlighting the highest common factors we get

6 (1,**2**,__3__,6)

8 (1,**2**,*4*,8)

12 (1,2,__3__,*4*,6,12) you forgot 6

To be honest this is all very long winded. Perhaps work at finding highest common multiples of two numbers and then move to doing problems like this after you are familiar with that.

Try questions like

Two different numbers, A and B have HCF's of 5, while A has a factor of 10. What are the lowest numbers that satisfy these conditions?