So,
To find the LCM, factor each number and then combine the factors.
P.F.F. of 120: [tex](2^{3})(3)(5)[/tex]
P.F.F. of 160: [tex](2^{5})(5)[/tex]
P.F.F. of 180: [tex](2^{2})(3^{2})(5)[/tex]
Combining them (and omitting overlaps) we get: [tex](2^5)(3^{2} )(5)\ or\ 1440[/tex]
The LCM of 120, 160, and 180 is 1440.
To find the HCF, factor (again) and find the common factors.
P.F.F. of 120: [tex](2^{3})(3)(5)[/tex]
P.F.F. of 160: [tex](2^{5})(5)[/tex]
P.F.F. of 180: [tex](2^{2})(3^{2})(5)[/tex]
Finding common factors: [tex](2^{2})(5)\ or\ 20[/tex]
The HCF of 120, 160, and 180 is 20.
