There are two common types of periodical cicadas the most...

Name: there are two common types of periodical cicadas the most prevalent is the 17 year cicada for which a brood of nymphs emerges from the ground to breed and lay eggs after a 17 year undergroun 09002
Uploaded: 2022-10-02T03:53:22-08:00
Duration: 7 min 2 s
Channel: Bailey Cooper
Description: there are two common types of periodical cicadas the most prevalent is the 17 year cicada for which a brood of nymphs emerges from the ground to breed and lay eggs after a 17 year undergroun 09002

There are two common types of periodical cicadas. The most prevalent is the 17-year cicada, for which a brood of nymphs emerges from the ground to breed and lay eggs after a 17-year underground wait. The 13-year cicada has a similar life cycle, but with a 13-year interval between one emergence and the next. Studies show that having a prime-number interval, such as 13 or 17, offers evolutionary advantages to each species. In particular, there is less interference between the two species when they live in the same region. (a) If broods of 13- and 17-year species happened to emerge in the same year, how many years will pass before this interference is repeated? (b) Suppose, hypothetically, that there exist 12- and 18-year species of cicadas. If both species happened to emerge the same year, in how many years will they interfere with one another again?

Transcript

00:01 Okay, so in this question, we have a question about different breeds of cicadas.

00:08 And we're wondering if they have different kind of life cycles and different intervals, yearly intervals by which they emerge.

00:18 When can two types emerge at the same time? so we have two different questions here.

00:27 Both of them are concerning basically what we're looking for when we're looking at.

00:31 For when can two different types emerge.

00:35 What we're looking for is the least common multiple, right? we want to know what's the least number of years.

00:45 Totally forgot what i was writing when i was writing it, my bad.

00:49 We're trying to find the least number of years in which they both occur at the same time.

00:56 That's just the least common multiple.

00:59 The way that we mathematically find this.

01:03 I kind of want to show it with the second example first.

01:08 So bear with me, i'm going to start with part b because it's a better example to illustrate how we find a least common multiple.

01:18 There's a few different ways that you can do it.

01:20 This way is helpful if you have really, really big numbers.

01:25 And so i'll show you a couple of different ways to do it.

01:27 This way is helpful, like i said, if you can't tell immediately what it's going to be, this can be helpful for you.

01:35 So in part b here, we're looking at a 12 -year species and an 18 -year species.

01:42 So let's get 12 on the board and let's get 18 on the board.

01:47 What we're going to want to do with these is break them down into their prime factorizations.

01:53 So basically break them down into factors until we're left with all prime numbers.

01:59 So for, for example, 12 can be broken down into 3 times 4, right? and 3 is a prime number, so we can circle it.

02:10 Then 4 can be broken down into 2 times 2.

02:14 And then those are both prime, so we can circle those.

02:18 And then we're done with 12, because we're just left with all those prime numbers.

02:23 18, we can break this down into 6 times 3.

02:28 3 is prime.

02:29 We can break this down into two times three.

02:34 And these are all prime.

02:37 So now that we have the prime factorizations, basically what you want to do in order to find the least common multiple is write out all of the factors, but only include duplicate factors once.

02:53 So what i mean by that is we have a three here and a three here.

02:58 So we're only going to include one three...

Question

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