what is the least common denominator?

It is the smallest number into which all of the denominators in a series of fractions can be evenly divided. For instance, is you have fractions
1/2, 2/3 and 5/6, the denominators are 2, 3 and 6, and the least common denominator is 6. The denominators 2, 3 and 6 can all be evenly divided into 6. There are larger common denomintors, such as 12, 18, 30, and 36, but 6 is the smallest one.

what is the LCD for1/6,2/5,3/7,3/5

To find the least common denominator (LCD) for 1/6, 2/5, 3/7, and 3/5, you need to identify the denominators and find the smallest number that they can all be evenly divided into.

The denominators are 6, 5, 7, and 5 respectively. To determine the LCD, you need to find the lowest common multiple (LCM) of these denominators.

To find the LCM, you can use multiple methods. One common approach is to list the multiples of each denominator until you find a common value.

For 6: 6, 12, 18, 24, 30, 36, ...
For 5: 5, 10, 15, 20, 25, 30, ...
For 7: 7, 14, 21, 28, 35, 42, ...

From these lists, you can see that the first number that appears in all three lists is 30. Therefore, the least common denominator (LCD) for 1/6, 2/5, 3/7, and 3/5 is 30.

So, when combining these fractions, you would convert each fraction to have a denominator of 30:

1/6 = 5/30
2/5 = 12/30
3/7 = 12/30
3/5 = 18/30

Now all the fractions have a common denominator of 30, and you can perform operations like addition or subtraction using these fractions.