Question

How do you find the LCM and HCF of `70 and 80`?

Answer 1

Use the product of the prime factors.

Explanation:

First write each number as the product of its prime factors. .
Then we know what we are dealing with.

For example, find the HCF and LCM of 70 and 80.
Write the same factors under each other:

`color(white)(xxxx)70 = 2color(white)(xxx.xx)xx5xx7`
`color(white)(xxxx)80 = 2xx2xx2xx5`

`HCF = color(white)(xx)2color(white)(xxxx.x) xx 5 " "= 10" "larr` multiply together

`LCM = " "2xx2xx2xx5xx7 = 280larr` multiply each column

From this it is clear that 70 and 80 have 2 common factors - 2 and 5.

The Highest Common Factor is the product of any common factors.

If we write the factors in index form we have exactly the same format that is used with variables in algebra.

`70 = (2)(5)(7) = 2*5*7`
`80 = (2^3)(5) = " "2^3*5`

The`HCF = 2xx5 = 10`

From this format we can also find the LCM with no extra working.

The `LCM = 2^3 xx5 xx7 = 280`

(Use the highest power of each prime number)

This is the easiest method I have ever come across. Hope it helps.