Respuesta :
Answer:
36 minutes
2 rounds for Priya
3 rounds for Ravish
Step-by-step explanation:
The answer is the LCM (least common multiple) of 12 and 18.
12 = 2^2 x 3
18 = 3^2 x 2
=>LCM of 12 and 18 = 2^2 x 3^2 = 4 x 9 = 36
=> After 36 minutes they meet again at the starting point
=> At that time, Priya has completed: 36/18 = 2 rounds
=> At that time, Ravish has completed: 36/12 = 3 rounds
After 36 minutes they meet again at the starting point.
In 36 minutes Priya and Ravish completed 2 and 3 rounds respectively.
What is least common multiple?
The least common multiple (L.C.M) of two numbers is the “smallest non-zero common number” which is a multiple of both the numbers.
What is prime factorization?
Prime factorization is defined as a way of finding the prime factors of a number, such that the original number is evenly divisible by these factors.
According to the given question.
Time taken by Priya to complete one round = 18 minutes
Time taken by Ravish to complete the one round = 12 minutes
Therefore,
The number of minutes taken by Priya and Ravish to meet again at the starting point when they start the race same time = L.C.M (12, 18)
Since,
Prime factorization of
[tex]12 = 2\times 2 \times 3[/tex]
And [tex]18 = 3 \times 3 \times 2[/tex]
⇒ L.C.M of 12 and 18 = 2 × 2 × 3 × 3 = 4 × 9 = 36
Hence, after 36 minutes they meet again at the starting point.
Now, number of round completed by Priya in 36 minutes = [tex]\frac{36}{18}= 2[/tex]
And the number of rounds completed by Ravish in 36 minutes = [tex]\frac{36}{12}[/tex] = 3
Hence, in 36 minutes Priya and Ravish completed 2 and 3 rounds respectively.
Find out more information about least common multiple and prime factorization here:
https://brainly.com/question/22813348
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