Question

What are the lcm and hcf of 120, 160, 180. Plz give the orders

Answer 1

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.