6 = 2*3
10 = 2*5
14 = 2*7
LCM(6,10,14) = 2*3*5*7 = 210
so, every 210 seconds they will blink at the same time
10 = 2*5
14 = 2*7
LCM(6,10,14) = 2*3*5*7 = 210
so, every 210 seconds they will blink at the same time
So let's see, the prime factors for each number are:
6 = 2 * 3,
10 = 2 * 5,
14 = 2 * 7.
To find the least common multiple, we take the highest power of each prime factor that appears in any of the numbers. So we have:
2^1, 3^1, 5^1, and 7^1.
Multiplying them together, we get:
2 * 3 * 5 * 7 = 210.
Therefore, the red, white, and green lights will wink together every 210 seconds. That's a lot of winking!
First, let's find the least common multiple (LCM) of 6, 10, and 14, which will give us the smallest number that is divisible by all three numbers.
The prime factors of 6 are 2 and 3.
The prime factors of 10 are 2 and 5.
The prime factors of 14 are 2 and 7.
We multiply the highest power of each prime factor, giving us:
2^1 * 3^1 * 5^1 * 7^1 = 2 * 3 * 5 * 7 = 210.
Therefore, the least common multiple (LCM) of 6, 10, and 14 is 210.
Thus, the three lights will wink together every 210 seconds.
Here's how you can find the LCM:
1. List the multiples of each interval until you find a common multiple:
- Multiples of 6: 6, 12, 18, 24, 30, 36, 42, ...
- Multiples of 10: 10, 20, 30, 40, ...
- Multiples of 14: 14, 28, 42, ...
2. Look for the smallest common multiple from the lists:
- In this case, we can see that 42 seconds is the smallest common multiple.
Therefore, the red, white, and green lights will wink together every 42 seconds.