Question

Lcm of 8,12,18,24??

Answer 1

`72`

Explanation:

Let's just continuously list the multiples of all of these numbers:

`8: 8, 16, 24, 32, 40, 48, 56, 64, color(blue)(72)...`

`12: 12, 24, 36, 48, 60, color(blue)(72), 84, 96, 108...`

`18: 18, 36, 54, color(blue)(72), 90, 108, 126, 144, 162...`

`24: 24, 48, color(blue)(72), 96, 120, 144, 168, 192, 216...`

The lowest number that we see repeating is `72`, thus this is our LCM.

Hope this helps!

Answer 2

`72`

Explanation:

The Least Common Multiple is the smallest possible number that is a product of two or more numbers. It is related to the Greatest Common Factor. Both are found by first factoring all of the numbers into their prime number factors. Recombining them calculated either the LCM or the GCF, as desired.
Factors:
`8 = 2xx2xx2`
`12 = 2xx2xx3`
`18 = 2xx3xx3`
`24 = 2xx2xx2xx3`

The LCM must include at least one of each factor. Because we have one (8) without a '3' factor, it must be multiplied by one of the others (the next lowest value). In practice, find the LCM by multiplying all unique prime factors: `2xx2xx2xx3xx3`
LCM `=72`
That is the least number that can be evenly divided by any of the numbers in the set.

Note that in comparison, the GCF is found by looking at the combinations of the prime factors - the only factor common to all of the numbers in this case is '2'.