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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What is the greatest number that will divide 209 and 347 leaving remainder 5 and 7 respectively?
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The HCF of 2091, 3485 and 4879 is x. The sum of the digits of x is:
If three numbers are in ratio of 3 : 5 : 7 and their LCM is 2415, what is the difference between the second number and the first number?
