GCF and LCM · part 5 of 7
Worked Examples
Why it took all of them, then the whole thing again with 18 and 30.
Why it took all of them
The LCM is one set of prime tiles. Both 24 and 36 are inside that one set, sharing most of the tiles. Here is the same set written out twice, marking the tiles each number needs.
One set of primes: 2 x 2 x 2 x 3 x 3 = 72, the LCM
The ones that make 24
2 x 2 x 2 x 3 = 24
The ones that make 36
2 x 2 x 3 x 3 = 36
Take any one tile away and one of the two numbers stops fitting. That is why 72 is the smallest number they both divide into. The 3 tiles marked in both rows multiply to 12, the GCF.
Again, with 18 and 30
Same three moves. Break both down, line them up, read the picture.
Breaking 18 down
18 = 2 x 3 x 3
Breaking 30 down
30 = 2 x 3 x 5
2 pairs, and 2 left over.
GCF = one from each pair = 2 x 3 = 6
LCM = one from each pair, then every leftover = 2 x 3 x 3 x 5 = 90
One set of primes: 2 x 3 x 3 x 5 = 90, the LCM
The ones that make 18
2 x 3 x 3 = 18
The ones that make 30
2 x 3 x 5 = 30