What is the LCM of 15, 6, and 9?

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Sep 3, 2017

Answer:

#LCM = 90#

Explanation:

Write each number as the product if its prime factors:

#color(white)(xxx)6= 2xx3#
#color(white)(xxx)9 =color(white)(xxx)3xx3#
#color(white)(xxx)15=color(white)(xx)3color(white)(xxx)xx 5#

#LCM = 2xx3xx3xx5 = 90#

OR, using the powers:

#6 = color(blue)(2) xx 3#
#9 = color(blue)(3^2)#
#15 = 3 xx color(blue)(5)#

To find the LCM, use the highest power of each base

#LCM = color(blue)(2xx3^2xx5) = 90#

Or just look at the multiples of #15# (the biggest number) until you find one which is even (because of 6) and divisible by #9# (Sum of the digits must be #9#)

#15,30, 45, 60, 75, color(blue)(90)#

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