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.