Question

Question #ac021

Answer 1

`40`.

Explanation:

Note first that 8 is a multiple of 4. Specifically, it is 2 times 4, aka 2 times 2 times 2, `2^3`. Thus, if we can find a denominator that has three 2s as factors, we will have found one that has both 8 and 4 as factors.

Now note that 10 has two factors, 5 and 2. It is that 2 that is most useful to us; it means that if we multiply 10 and 4, we will be multiplying 5, 2, 2, and 2. This result has all the factors for 10, 4, and 8, and is the lowest number to have those factors. Thus, this is our lowest common denominator.

Answer 2

40

Explanation:

To get this, we must first realize that 3/4, 5/8, and 1/10 all have prime numerators, so we cannot get a common denominator lower than 10 by division (e.g. if we had 4/4, 4/8 and 15/10 we could reduce to get 2/2, 1,2, 3/2, but we can't reduce here).

Also, it cannot be 10, since 4 doesn't multiply (with integers) to 10.

Now, we just take multiples of 10 and find one that works for all of them.

20?

We can't make 8 multiply to 20, so no.

30?

Doesn't work for 8 or 4.

40?

Yes! (4x10, 8x5, 10x4)