Question

How do find the LCM of 27 and 45 by listing multiples?

Answer 1

`LCM=45`

Explanation:

#{: (color(blue)27=,color(white)("xx"),color(blue)3xx,color(gray)9,,,), (,,,color(blue)3color(blue)xx,color(blue)3,,), (color(blue)45=,color(white)("xx"),color(blue)3xx,color(grey)15,,,), (ul(color(white)(LCM=)),,ul(color(white)(3xx)),ul(color(blue)3xx),ul(color(white)(3xx)),ul(color(blue)5),), (LCM=,color(white)("xx"),3xx,3xx,3xx,5,=45) :}#

Answer 2

`135.`

Explanation:

Let `M_27` denote the set of (positive) multiples of `27.`

`:. M_27={27,54,81,108,135,162,189,216,243,270,...}.`

Similarly, `M_45={45,90,135,180,225,270,...}.`

`:. M_27 nn M_45={135,270,...}.`

The LCM of `27 and 45=minM_27nnM_45=135.`