Fractions
We have the fractions:
2/5 and 3/10
The denominators of the fractions are 5 and 10.
We need to find a common number for 5 and 10. There are several numbers that are common multiples of both 5 and 10. We only need to find the first multiples of each:
5 , 10 , 15 , 20 , 25 , 30 , ...
10 , 20 , 30 , 40 , ....
We can see the numbers {10,20,30,...} are common multiples of 5 and 10. We can select any of those as our solution, but we prefer to pick the first one: 10.
To find 10 out of 5, we need to multiply it by 2, thus the whole fraction must be multiplied by 2:
2/5 = 4/10
Now 4/10 and 3/10 have a common denominator.
As mentioned, we have found the least possible denominator, but there are many others.