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
The HCF and LCM of two numbers are 12 and 72, respectively. If the ratio of the two numbers is 2 ∶ 3, then the larger of the two numbers is:
Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.
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What is the least number which when divided by 12,20 and 24 leaves in each case a remainder of 8?
Which of the following is a pair of co-primes?
