Question

What is the least common denominator for 5/6 and 3/8. 3/4 and 6/7

Answer 1

$\frac{5}{6}\\\\the\ denominator\ is\ 6\\\\list\ the\ multiples\ of\ 6:\ 0;\ 6;\ 12;\ 18;\ \fbox{24};\ 30;\ 36;...\\\\\frac{3}{8}\\\\the\ denominator\ is\ 8\\\\list\ the\ multiples\ of\ 8:\ 0;\ 8;\ 16;\ \fbox{24};\ 32;...\\\\LCD\left(\frac{5}{6};\ \frac{3}{8}\right)=24$


$other\ mthod\\\\\frac{3}{4}\\\\the\ denominator\ is\ 4=2\cdot2\\\\\frac{6}{7}\\\\the\ dominator\ is\ 7=7\\\\LCD\left(\frac{3}{4};\ \frac{6}{7}\right)=2\cdot2\cdot7=28$

$First\ example:\\\\6=\fbox{2}\cdot3\\\\8=\fbox{2}\cdot2\cdot2\\\\LCD\left(\frac{5}{6};\ \frac{3}{8}\right)=2\cdot2\cdot2\cdot3=24$

Answer 2

You need to find the least common multiple of the denominators. Check:
6+6=12     6+6+6=18      6+6+6+6=24    ....
8+8=16     8+8+8=24      8+8+8+8=32    ....
Now we see that the least common multiple is: 24.

Similarly, we proceed to the second:
4+4=8       4+4+4=12     4+4+4+4=16     4+4+4+4+4=20      4+4+4+4+4+4=24    4+4+4+4+4+4+4=28     ....
7+7=14     7+7+7=21     7+7+7+7=28 .....
again, we see that the least common multiple is: 28.