Question

list the first five multiples of the denominator in each fraction in order of least to greatest.

fraction multiples
$\frac{1}{6}$ 6 12 $square$ $square$ $square$
$\frac{3}{4}$ $square$ 8 $square$ 16 $square$

what is the least common denominator for the two fractions?
$square$

Explanation:

Step1: Find multiples of 6

The denominator of \(\frac{1}{6}\) is 6. The first five multiples of 6 are calculated as:
\(6\times1 = 6\), \(6\times2 = 12\), \(6\times3 = 18\), \(6\times4 = 24\), \(6\times5 = 30\). So the missing multiples for \(\frac{1}{6}\) are 18, 24, 30.

Step2: Find multiples of 4

The denominator of \(\frac{3}{4}\) is 4. The first five multiples of 4 are:
\(4\times1 = 4\), \(4\times2 = 8\), \(4\times3 = 12\), \(4\times4 = 16\), \(4\times5 = 20\). So the missing multiples for \(\frac{3}{4}\) are 4, 12, 20.

Step3: Find least common denominator (LCD)

To find the LCD of 6 and 4, we list their multiples:
Multiples of 6: 6, 12, 18, 24, 30,...
Multiples of 4: 4, 8, 12, 16, 20,...
The smallest number common to both lists is 12.

Answer:

For \(\frac{1}{6}\) multiples: 18, 24, 30
For \(\frac{3}{4}\) multiples: 4, 12, 20
Least common denominator: 12