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Mentallic

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Let's list out the multiples of 5 and 6 to illustrate this:

5, 10, 15, 20, 25, 30, 35, 40, ....

6, 12, 18, 24, 30, 36, 42, ....

Notice that the first number to appear in both of these lists is 30. This means that 30/5 is an integer, and so is 30/6.

Now let's look at 6 and 12

6, 12, 18, 24, 30, ...

12, 24, 36, ....

The first number is 12. See how the numbers sort of overlap? 6 goes into 12, so when you list the multiples of 6 and 12, you'll get a small LCM number (unlike with 5 and 6 which didn't happen for a little while).

If the Highest Common Factor (HCF) of two numbers is 1, then the LCM of the two numbers is their product.

Factors of 5 and 6:

5 = 1, 5

6 = 1, 2, 3, 6

The largest number in both of these lists is only 1, which means that 5 and 6 have no common factors, so you need to multiply the two numbers to make the denominator equal.

Factors of 6 and 12:

6 = 1,2,3,6

12 = 1,2,3,4,6,12

The largest in both of these lists is 6, so this means that the LCM of the two numbers is going to be less than 6*12 = 72. Since the HCF is 6, then the LCM is 6*12 / 6 = 12.

Another example:

9 and 15. The factors are

9 = 1,3,9

15 = 1,3,5,15

The HCF is 3, so the denominator you are aiming for is going to be 9*15/3 = 9*5 = 45.

Checking the multiples of 9 and 15:

9,18,27,36,45, ...

15,30,45, ...

45 is the first to appear, so it seems to work.

- #3

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5/6 + 7/12 = (60 + 42)/72

Will give you the same answer as

5/6 + 7/12 = (10 + 7)/12

If you reduce both fractions to their lowest form, of course. Try simplifying those two answers above and see if you get the same result.

Which way did you find easier?

- #4

Mark44

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Based on your post here and another one a day or two ago, it appears to me that your arithmetic skills need some work, particularly those related to working with fractions. I would advise you to spend some time refreshing them. Khanacademy would be a good place to start -- http://www.khanacademy.org/math/arithmetic/fractions.

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