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