Question

What are all the LCM ( least common multiples ) of 15,20 and 25 ?

Answer 1

The common multiples are `300, 600, 900, 1200, 1500.....`

But there is only ONE that is the LOWEST of them all: `300`

Explanation:

Groups of numbers can have many common multiples, but there is only ONE lowest common multiple.

Write each number as the product of its prime factors:

`" "15 = color(white)(wwww)3xx5`
`" "20 = 2xx2color(white)(w.)xx5`
`" "25=ul(color(white)(wwwww.w)5xx5)`
`LCM = 2xx2xx3xx5xx5 = 300`

The LOWEST multiple must have all the factors of numbers, but without any duplicates.

Common multiples are: `300, 600, 900, 1200, 1500 ....`etc.

However, `300` is the only lowest one.

Answer 2

15 = 3 x 5
20 = 2 x 2 x 5
25 = 5 x 5

Now, we need the highest powers of each factor that occurs

i.e. 2 x 2 x 3 x 5 x 5 => 300

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