What's the LCM of 6 and 8?

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Answer 1 · 2018-05-20T12:01:48

#LCM=24#

Express both numbers as prime factors,

#6=2*3#

#8=2^3#

Hence, the lowest common multiple would consist of the highest degree of prime numbers in the two numbers.

Since the highest degree of #2# is #2^3# found in #8# and the highest degree of #3# is #3^1# found in #6#,

#LCM=2^3*3#
#color(white)(LCM)=24#

This method does not work for only two numbers but also work with three or more complicated numbers as well.

For example, LCM of #68#, #98# and #102#,

#68=2^2*17#

#97=2*7^2#

#102=2*3*17#

Hence,

#LCM=2^2*3*7^2*17#
#color(white)(LCM)=9996#