Question #fb025

The lowest common multiple of two numbers is the smallest number both will divide into exactly.

For instance

`lcm(2,3)=6`

because 6 is the smallest number that BOTH `2 " & "3` will divide into

there are several methods to go about find the `LCM`
here I will illustrate just two

method 1

The simplest way is just to write down the multiples of both numbers and then pick out the common ones and hence the lowest is identified easily.

lcm(4,12)#

multiples of `4:{4,8,color(red)(12),16,20,color(red)(24),28,32,color(red)(36)...}`

multiples of `12:{color(red)(12,24,36),...}`

the common multiples are highlighted in red

common multiples`{12,24,36,...}`

`:.lcm(4,12)=12.`

method 2

for two numbers `a,b`

The second method uses the relationship

`axxb=hcf(a,b)xxlcm(a,b)`

this is particularity useful when the numbers are too large for listing the multiples.
so

`lcm(25,35)`

`hcf(25,35)=5`

`:.25xxcancel(35)^7=cancel(5)xxlcm(25,35)`

`lcm(25,35)=25xx7=175`

the third method using prime factors has been covered elsewhere

L C M : The smallest positive number that is a multiple of two are more numbers.
L C M of 3 & 5 is 15, because 15 is a multiple of 3 & 5. Other common multiples include 30, 45, etc., but they are not the smallest.

To find the L C M of 4, 10 :
Multiples of 4 are 4 8 12 16 20 24 28 32 36 40 and so on.
Factors of 10 = 10 20 30 40 50 60 and so on.
There is a match @ 20 which is the least common multiple.