Three automatic doors in a metro station undergo system checks at regular intervals of 14 minutes, 18 minutes, and 21 minutes, respectively. If all three doors are checked together at the start, after how many minutes will they be checked together again for the first time?
126 minutes
The three doors are checked together again after a time equal to the LCM of their intervals 14, 18 and 21 minutes.
Write each as prime factors: \(14 = 2 \times 7\), \(18 = 2 \times 3^2\), \(21 = 3 \times 7\).
Take the highest power of each prime: \(2^1 \times 3^2 \times 7^1 = 2 \times 9 \times 7 = 126\).
Hence, all three doors are checked together again after 126 minutes.
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Important Questions from LCM and HCF
Six bells begin to toll together and toll, respectively, at intervals of 3, 4, 6, 7, 8 and 12 seconds. After how many seconds, will they toll together again?
A and B are two prime numbers such that A > B and their LCM is 209. The value of A 2 - B is:
Find the least number which when divided by 12, 18, 24 and 30 leaves 4 as remainder in each case, but when divided by 7 leaves no remainder.
Calculate the HCF of \(\frac{12}{5}\) , \(\frac{14}{15}\) and \(\frac{16}{17}\) .
Three numbers are in the proportion of 3 : 8 : 15 and their LCM is 8280. What is their HCF?
