Find the least common denominator for the given set of denominators.
-84, 378
A)42
B)1,512
C)2,268
D)756

Question

Quizplus · Accepted Answer

To find the least common denominator, we need to find the smallest number that both 84 and 378 divide into evenly. We can begin by listing the multiples of 84 and seeing which ones are also multiples of 378:
84, 168, 252, 336, 420, 504, 588, 672, 756, 840, ...
378, 756, 1134, 1512, ...
We can see that the least common multiple of 84 and 378 is 756, which is D in our answer choices. The LCM of 84 and 378 can be found by prime factorizing each number: 
84 = 2^2 x 3 x 7  
378 = 2 x 3^3 x 7

We need to choose the highest power of each prime number that appears in either factorization.  
So the LCM = 2^2 x 3^3 x 7 = 756.

Find the Least Common Denominator for the Given Set of Denominators