Find the least common multiple for 4 and 5.(1 point)
The least common multiple of 4 and 5 is 20.
Find the least common multiple of 7 and 11.(1 point)
The least common multiple of 7 and 11 is 77.
Find the least common multiple of 8 and 12.
To find the least common multiple (LCM) of 8 and 12, we can use the prime factorization method.
Prime factorization of 8: 2 x 2 x 2
Prime factorization of 12: 2 x 2 x 3
To find the LCM, we take the highest power of each prime factor that appears in the factorization of either number:
2^3 x 3 = 8 x 3 = 24
Therefore, the least common multiple of 8 and 12 is 24.
Marisol and Paul start walking a circular path repeatedly at the same time. Marisol can walk around the path in 12 minutes, and Paul can do it in 9 minutes. How many minutes will they have to walk until they are both back at the beginning of the path at the same time?(1 point)
minutes
To find out when both Marisol and Paul will be back at the beginning of the circular path at the same time, we need to find the least common multiple (LCM) of their walking times.
The LCM of 12 and 9 can be found by prime factorization.
Factorizing 12: 2 x 2 x 3
Factorizing 9: 3 x 3
To find the LCM, we take the highest power of each prime factor that appears in either number:
2^2 x 3^2 = 4 x 9 = 36
Therefore, Marisol and Paul will both be back at the start of the path after walking for 36 minutes.
At Howard High School, the football team and the lacrosse team both had a game today. The football team has a game every 7 days, and the lacrosse team has a game every 4 days. In how many days will they both have a game on the same day again?(1 point)
days
To find the number of days until both teams have a game on the same day again, we can find the least common multiple (LCM) of 7 and 4.
The LCM of 7 and 4 can be found by prime factorization.
Factorizing 7: 7
Factorizing 4: 2 x 2
To find the LCM, we take the highest power of each prime factor that appears in either number:
2 x 2 x 7 = 28
Therefore, both teams will have a game on the same day again in 28 days.