Let the two numbers be say #8# and #36#.
Write out the prime factors of each number.
#8=color(red)(2xx2)xx2#
#36=color(red)(2xx2)xx3xx3#
Observe that #color(red)(2xx2)# are common to both. Observe this is #HCF# of two numbers.
What are others? #color(purple)2# is remaining in first and #color(green)(3xx3)# remain in second.
Multiply all to get LCM i.e. LCM is
#color(red)(2xx2)xxcolor(purple)2xxcolor(green)(3xx3)=72#
Simiilarly, let the three numbers be #8#, #12# and #20# and then
#8=color(red)(2xx2)xx2#
#12=color(red)(2xx2)xx3#
#20=color(red)(2xx2)xx5#
Observe that #color(red)(2xx2)# are common to the three. Observe this is #HCF# of three numbers.
What are others? #color(purple)2# is remaining in first, #color(green)3# remains in second and #color(blue)5# remains in the third number.
LCM is #color(red)(2xx2)xxcolor(purple)2xxcolor(green)3xxcolor(blue)5=120#
