If you always get it hard to understand the basics idea in finding L.C.M of any given fractions, do not worry I'm here to brake every thing into pieces but you need to study the simplemethod123 pattern. First what do you understand by the term (L.C.M) this simply means (least common multiple).
Multiples is the time table of that number, multiple of 2: 2x1 =2, 2x2 = 4, 2x3 = 6, 2x4 = 8 etc.
There are repeated numbers in multiplication table, they appear in multiple of numbers, example:
2 x 2 = 4
4 x 1 = 4
Also
3 x 4 = 12
6 x 2 = 12
12 x 1 =12
and so on, now you can see some repeated numbers we have a lots of them,you can discover more of these numbers. Common means the smallest among others of the same group. This is what i mean:
2: 2 x 1 = 2 , 2 x 2 = 4 , 2 x 3 = 6 , 2 x 4 = 8 , 2 x 5 = 10, 2 x 6 = 12 , 2 x 7 = 14 , 2 x 8 =16 ,2 x 9 = 18 , 2 x 10 = 20 , 2 x 11 = 22, 2 x 12 = 24 etc.
3: 3 x 1 = 3, 3 x 2 = 6 , 3 x 3=9, 3 x 4= 12, 3 x 5 =15, 3 x 6 = 18, 3 x 7 = 21, 3 x 8 = 24 etc.
Now take a look at the above two numbers 2 and 3
in 2's we have:6,12,18 and 24 -------- 6
in 3's we have: 6,12,18 and 24----------6
the L.C.M of 2 and 3 is 6 because it is the smallest/least number among many, they are still others when multiplied further.
2 x 3 = 6
So, when facing this kind of issues put the numbers in its multiple form, the first number that will appear in the given whole numbers or fractions ( denominator) is the L.C.M. Lets find some least common multiple of some fractions
Examples
find the L.C.M of:
1 2 1 1
-------, ------- ,-------- , -------- L.C.M of (8,4,2,6) = 24
8 4 2 6
Working
Multiple of (8,4,2 and 6)
8: 8, 16 , 24 .......
4: 4, 8 ,12 , 16 , 20 , 24 ......
2: 2 , 4 , 6 , 8 , 10 , 12 , 14 , 16 , 18 , 20 , 22 , 24 ...
6: 6 , 12 , 18 , 24 , 30 , 36 ........
We say, 24 is the L.C.M of (8,4,2,6), because it appears first in both multiple of the given denominator. To find any L.C.M of any number deal with the bottom number, either its fractions or a whole number used division method. There is no way you can obtain an equivalent fraction excerpt dealing with the bottom numbers, now let look at some examples.
Something like this:
3 1
--------- and --------
5 2
we are to find the L.C.M of 5 and 2, do not forget finding L.C.M is about multiplying the given numbers.
We say 5: 5 x 1 = 5 , 5 x 2= 10 , 5 x 3 = 15, 5 x 4 = 20 .......
2: 2 x 1 = 2 , 2 x 3 = 6 , 2 x 4 = 8 , 2 x 5 = 10 , 2 x 6 = 12 ,......
L.C.M of 2 and 5 = 10
The L.C.M of 2 and 5 is 10. If you continue multiplying the numbers, you'll still discover more common multiples of 2 and 3. At least you should understand what L.C.M is.
Lets find the L.C.M of :
3 4 2 1
--------- , -------- , --------- , --------
. 5 15 3 2
We will find the multiple of 5 , 15 , 3 , and 2
5: 5 x 1 = 5 , 5 x 2 = 10 , 5 x 3 = 15 , 5 x 4 , = 20 , 5 x 5 = 25 , 5 x 6 = 30 , 5 x 7 = 35..........
15 : 15 x 1 = 15 , 15 x 2 = 30 , 15 x 4 = 45.....
3 : 3 x 1 = 3 , 3 x 2 = 6 , 3 x 3 = 9 , 3 x 5 = 15 , 3 x 6 = 18 , 3 x 7 = 21 , 3 x 8 = 24 , 3 x 9 =27 3 x 10 = 30......
2 : 2 x 1 = 2 , 2 x 2 = 4 , 2 x 3 = 6 , 2 x 4 = 8 , 2 x 5 = 10 , 2 x 6 = 12 , 2 x 7 = 14, 2 x 8 = 16 , 2 x 9 = 18 , 2 x 10 = 20 , 2 x 11 = 22 , 2 x 12 = 24 , 2 x 13 = 26 , 2 x 14 = 28 , 2 x 15 = 30......
Take a look at the above denominators, we found 30 as that Least Common Multiple. Hope you understand the concept of L.C.M
Find the L.C.M of the following denominators
1 1 3 7 5
1. ------, -------,------- , ------- ,--------
3 4 8 24 12
5 7 1
2. --------, ---------, -------
12 8 2
1 2 3 3
3. -------, ---------, --------, ---------
2 3 4 5
If you have any question on these, please put them in the comments box.
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