The next time that the trains from both lines will arrive simultaneously, using their least common multiple, is <u>7:56 A.M</u>.
<h3>What is the least common multiple?</h3>
The least common multiple (LCM) is the smallest number of a multiple of two or more numbers.
For instance, the LCM of 8 and 14 is 56. The LCM shows that in 56 minutes from 7:00 A.M., the orange line must have arrived 4 times (14 x 4 = 56), while the green line must have arrived 7 times (8 x 7 = 56).
<h3>Data and Calculations:</h3>
Orange Line Green Line
Arrival Time 14 minutes 8 minutes
The time that they arrive together is 7:00 A.M.
The least common factor of 14 and 8 is 56 because
8 = 2 × 2 × 2
14 = 2 × 7
LCM (8, 14) = 2 × 2 × 2 × 7 = 56
The number of times that the Orange Line will arrive in 56 minutes, taking 14 minutes per arrival is <u>4 times</u> (56/14).
The number of times that the Green Line will arrive in 56 minutes, taking 8 minutes per arrival is <u>7 times</u> (56/8).
Thus, the next time that the trains from both lines will arrive simultaneously is <u>7:56 A.M</u> (7:00 A.M. + 56 minutes).
Learn more about the Least Common Multiple at brainly.com/question/16054958
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