Fractions from least to greatest

Question

What is the fastest way to find the least common denominator of all the fractions without losing too much time?

7/9 , 1/4, 14/15, 2/3, 1/2

Thanks.

Answer 1

NOTE: Your title does not ask the same as the body. I am answering the body.

Decompose each denominator : $$9 = 3^2, \quad 4 = 2^2, \quad, 15 = 3\cdot5, \quad 3 = 3, \quad 2 = 2$$

You least common denominator is the lowest common multiple hence by inspection we deduce it's: $$2^2\cdot3^2\cdot 5 = 4\cdot 9\cdot 5 = 180$$

Answer 2

I don't have 50 rep, so I make an anwser, but I know it does not merit one. You just have to see what is 1- each of these fraction. It is in this case an easier way of "seeing" the order.