Question

One firefly flashes every 8 seconds. Another firefly flashes every 10 seconds. Both fireflies just flashed. After how many second will both fireflies flash at the same time again? (I know it's somehow related to LCM, GCF, Prime factorization)

Answer 1

40 sec

Explanation:

So here we want to find the LCM of 8 and 10

➝ 8 = 2×2×2 = 2³

➝ 10 = 2×5

LCM(8,10) = 2³×5 = 40

So they will flash again after 40 sec.

Answer 2

Explanation:

You're correct that this problem involves finding the least common multiple (LCM) of 8 and 10, which will give us the number of seconds after which both fireflies will flash at the same time again.

To find the LCM of 8 and 10, we can use their prime factorizations:

8 = 2^3

10 = 2 × 5

The LCM of 8 and 10 is the product of the highest powers of all the prime factors involved, which in this case are 2^3 and 5. Therefore:

LCM(8, 10) = 2^3 × 5 = 40

So after 40 seconds, both fireflies will flash at the same time again. We can check this by dividing 40 by each of the individual flash intervals to see if we get a whole number:

40 ÷ 8 = 5

40 ÷ 10 = 4

Both of these divisions result in whole numbers, which confirms that 40 is the least common multiple of 8 and 10. Therefore, both fireflies will flash at the same time again after 40 seconds.