Multiples that #8# room #8,16,24,32,40,48,56,64,72,80,88,96,104,112,120,128,136,144......#

Multiples that #12# space #12,24,36,48,60,72,84,96,108,120,132,144......#

Multiples of #18# room #18,36,54,72,90,108,126,144......#

Hence usual multiples room #72,144,.......#

and Least common Multiple is #72#

Another shorter means is to write numbers as multiplication the its element factors

#8=2xx2xx2# #-># #2# comes three times

#12=2xx2xx3# #-># #2# come twice and #3# once.

You are watching: Least common multiple of 8 and 18

#18=2xx3xx3# #-># #2# come once and also #3# twice

So maximum times is 3 times because that #2# and also two times because that #3#.

Hence, Least common Multiple is #2xx2xx2xx3xx3=72#.

Tony B
Apr 9, 2018

Use Shwetyank"s an approach in the class and an exam. The marking schema will be collection up for the approach.

#color(blue)("My different approach - helps with understanding.")#

Explanation:

Target: LCM that 8,12 and 18.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~#color(magenta)("Once you are used to this it have to look like")##color(magenta)("what complies with (for these numbers).")#

#12=color(white)("d")8+4 color(white)("d") ->2xx4=color(white)(..)8" therefore "2xx12=24##24=18+6 color(white)("d")->3xx6=color(white)(.)18" so "color(white)(.)3xx24=72#

#"LCM "=72#

3 currently inclusive that the answer because that 3 relationships

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There are numerous ways of writing any certain value for this reason we deserve to make it look yet we wish as long as final outcome is the correct value. Example: 6 can and may be created as #5+1# if we so chose.

See more: Mass Of A Piece Of Paper Sizes In Grams, Everyday Life

#color(brown)("Dealing through the 8 and also 12 part")#

Write 12 together #8+4#

Now we begin counting the 12"s but make sure it encompasses the 8 + 4"s. Once we have gathered enough 4"s to make another eight we have uncovered the least common factor of 8 and 12

#1: -> color(green)(12)=color(red)(8)+4##2:-> ul(color(green)(12))=color(red)(8)+ul(4 larr" include the 12"s and the 4"s")##color(white)("ddddd")color(green)(24) color(white)("ddd")ul(color(white)("ddd")color(red)(8))##color(white)("dddddddddddd")color(red)(24) larr" including all the 8"s"#

#2" the "12=24##3" the "color(white)("d")8=24#

So LCF (for 8 and 12) is 24

So we have a fixed proportion of 8 and also 12 in ~ every amount of 24. Consequently any other product of components will need to include some lot of of 24~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~#color(brown)("Dealing through the 18 part")#

As the value of 24 locks with each other the counts of 8 and also 12 we lug that forward.

Write the 24 as #18+6#

We are now counting the 24"s

#1: ->color(green)( 24)=color(red)(18)+6##2: ->color(green)(24)=color(red)(18)+6##3:->ul(color(green)(24))=color(red)(18)+ul(6larr" include the 24"s and also 6"s")##color(white)("ddddd") color(green)(72)color(white)("dddddd")ul(color(red)(18))larr" add all the 18"s"##color(white)("ddddddddddddd")color(red)(72)#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~#color(magenta)(" LCM "= 72)#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~