Question

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

Answer 1

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.

Answer 2

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



`other\ mthod\\\\(3)/(4)\\\\the\ denominator\ is\ 4=2\cdot2\\\\(6)/(7)\\\\the\ dominator\ is\ 7=7\\\\LCD\left((3)/(4);\ (6)/(7)\right)=2\cdot2\cdot7=28`


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