What is the LCM of 45, 28, and 150?

1 Answer
EZ as pi
May 9, 2017

LCM = 2xx2xx3xx3xx5xx5xx7 = 6300

Explanation:

Write each number as the product of its prime factors. In this way you know exactly what you are working with, which factors are common and how many of each you need for the LCM.
Line up like factors under each other.

color(white)(.......)45 = color(white)(...........)3xx3xx5
color(white)(.......)28 = 2xx2color(white)(.......................)xx7
color(white)(......)ul(150 =2color(white)(..........)3color(white)(......)xx5xx5" ")
color(white)(.)LCM = 2xx2xx3xx3xx5xx5xx7 = 6300

Notice that in order for:

28 to be a factor, there must be two 2s and "one " 7
45 to be a factor, there must be two 3s
150 to be a factor, there must be two 5s

The LCM is the product of all the factors, but without the duplicates.

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