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5 and 6 and 3 and 10, the pairs of numbers that have a least common multiple of 30.
<u>Step-by-step explanation:</u>
Case 1: LCM (3, 6)
Prime factorization of 3:
Prime factorization of 6:
Using all prime numbers found as often as each occurs most often we take
Therefore LCM (3, 6) = 6.
Case 2: LCM (5, 6)
Prime factorization of 5:
Prime factorization of 6:
Using all prime numbers found as often as each occurs most often we take
Therefore LCM (5, 6) = 30
Case 3: LCM (3, 10)
Prime factorization of 3:
Prime factorization of 10:
Using all prime numbers found as often as each occurs most often we take
Therefore LCM (3, 10) = 30
Case 4: LCM (5, 10)
Prime factorization of 5:
Prime factorization of 10:
Using all prime numbers found as often as each occurs most often we take
Therefore LCM (5, 10) = 10
Answer:
Levi's dad takes 1.67 hours to wash the car by himself
Step-by-step explanation:
* Lets explain how to solve the problem
- Levi takes 2.5 hours to wash his dad's car alone
- Levi and his dad take 1 hour to wash the dad's car together
∵ Levi takes 2.5 hours to wash the car alone
∴ The rate of Levi is 1/2.5 car/hr
∵ His dad takes x hours to wash the car alone
∴ The rate of his dad is 1/x car/hr
∵ They working together for 1 hour to wash the car
- The equation of the work is rate of Levi × t + rate of his dad × t = 1
∵ t is the time of working together
∵ t = 1 hour
∴
- Multiply both sides by 2.5x to cancel the denominators
∵
∵ 1 × (2.5x) = 2.5x
∴ x + 2.5 = 2.5x
- Subtract x from both sides
∴ 2.5 = 1.5x
- Divide both sides by 1.5
∴ x = 5/3 ≅ 1.67
∵ x is the the time of his dad to wash the car alone
∴ Levi's dad takes 1.67 hours to wash the car by himself