one lighthouse light flashes every 26 seconds, and a second lighthouse light flashes every 30 seconds. if they both flash at the same moment, how long will it be until they will flash together again
To find out when the two lighthouse lights will flash together again, we need to find the least common multiple (LCM) of 26 and 30.
The prime factors of 26 are 2 and 13.
The prime factors of 30 are 2, 3, and 5.
To find the LCM, we need to take the highest power of each prime factor that appears in either number:
2^1, 3^1, 5^1, 13^1.
Multiplying these prime factors together, we get:
2 * 3 * 5 * 13 = 390.
Therefore, the two lighthouse lights will flash together again after 390 seconds or 6 minutes and 30 seconds.
To find out how long it will be until both lighthouse lights flash together again, we need to determine the time at which their flashing patterns align.
To do this, we need to find the least common multiple (LCM) of the two flashing intervals, which in this case are 26 seconds and 30 seconds.
To find the LCM, you can follow these steps:
Step 1: List the multiples of each flashing interval:
- Multiples of 26 seconds: 26, 52, 78, 104, 130, 156, 182, 208, 234, 260, ...
- Multiples of 30 seconds: 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, ...
Step 2: Identify the smallest common multiple in both lists.
- The multiples of 26 and 30 overlap at 390 seconds.
Therefore, the two lighthouse lights will flash together again after 390 seconds or 6 minutes and 30 seconds.
To determine when the two lighthouse lights will flash together again, we need to find the least common multiple (LCM) of their flash intervals, which are 26 seconds and 30 seconds.
Step 1: Find the prime factors of each interval.
26 = 2 * 13
30 = 2 * 3 * 5
Step 2: Identify the highest power of each prime factor.
The prime factors and their highest powers for 26 and 30 are:
2^1, 3^0, 5^0, 13^1
Step 3: Multiply the prime factors with their highest powers.
2^1 * 3^0 * 5^0 * 13^1 = 2 * 1 * 1 * 13 = 26
Therefore, the LCM of 26 seconds and 30 seconds is 26 seconds. This means that the two lighthouse lights will flash together again after 26 seconds.