We continued our work with least common multiples (LCM). The problem today included determining when 13-year and 17-year cicadas would both emerge from the ground. The way you would find out is much like what we did earlier.
13x1=13 17x1=17
13x2=26 17x2=34
13x3=39 17x3=51
We would do this until we found multiples that match. In this case:
13x17=221 17x13=221
When the two numbers or factors of the two numbers are relatively prime, we can see that the numbers multiplied together often represent the least common multiple. This is true 95% of the time. Here are two counterexamples:
2x1=2 4x1=2
2x2=4 4x2=8
2x3=6 4x3=12
2x4=8 4x4=16
Here we see that 2x4 is 8, but the cycle would happen sooner, at an interval of 4. Let's look at 4 and 6 now.
4x1=4 6x1=6
4x2=8 6x2=12
4x3=12 6x3=18
4x4=16 6x4=24
4x5=20 6x5=30
4x6=24 6x6=36
As you can see, 24 is a multiple of 6 and 4 (4x6) but the interval that would happen sooner would be 12 which is the LCM of 4 and 6.
When finding LCM, it is helpful to list in order each number times 1-? to determine the LCM. Yes it is work but barring any mathematical errors, this method will always work.
No comments:
Post a Comment