My question is: What is the least common denominator for 1/5, 1/4 and 1/9?

Question

across · Answer

A good idea would be to factor each number into their prime powers.

$5=2^0\cdot3^0\cdot5^1$
$4=2^2\cdot3^0\cdot5^0$
$9=2^0\cdot3^2\cdot5^0$

Since you are trying to find $\gcd(5,4,9)$, you multiply the minimum of each prime power.

$2^0\cdot3^0\cdot5^0=1$

In other words, $5,4,9$ are pairwise coprime.

anonymous · Answer

I see what you are explaining.. But the answer is 180 as the LCD... How can I get to this number the fastest?

across · Answer

Oh, sorry. I got carried away: what you're trying to find is the $\text{least common multiple}$. In that case, you multiply the greatest prime powers:

$2^2\cdot3^2\cdot5^1=4\cdot9\cdot5=180$

anonymous · Answer

oh yes thats right. I am reviewing my math for the ACT placement test so I am having to refresh my math skills... :( I am not as good as most in math.. Really appreciate your help!