Examkin

Question

Difficulty: EasyFactors, Multiples, and Primes

A flashing red light blinks every 1212 seconds, and a flashing blue light blinks every 1515 seconds. If both lights blink together at exactly 8:00 PM, how many seconds will pass before they blink together again?

  1. A
    3
  2. B
    27
  3. 60Answer
  4. D
    180

Answer

60
To find when two periodic events will occur together again, the least common multiple (LCM) of their individual intervals must be determined. The LCM of 1212 and 1515 is 6060, meaning the lights will blink together every 6060 seconds.

Step-by-Step Solution

1
Identify the goal of the problem.
Find the Least Common Multiple (LCM) of the two blinking intervals to determine when the lights will sync up again.
Because the lights blink periodically, their next simultaneous blink occurs at a common multiple of both intervals.
2
Find the prime factorization of 12 and 15.
12=22×312 = 2^2 \times 3, and 15=3×515 = 3 \times 5.
Prime factorization is a reliable method for finding the LCM.
3
Calculate the LCM using the prime factors.
LCM=22×3×5=4×3×5=60LCM = 2^2 \times 3 \times 5 = 4 \times 3 \times 5 = 60.
The LCM is calculated by multiplying the highest power of each prime factor present in either number.

Key Concept

Least Common Multiple (LCM) applied to periodic events
Rate this question

Topics

Factors, Multiples, and Primes

More questions from this topic