LOWEST COMMON MULTIPLE (LCM)
Problem 1:
Question: Two buses leave the same station at 8:00 AM. The first bus returns to the station every 30 minutes, and the second bus returns every 45 minutes. At what time will both buses return to the station together?
Problem 2:
Question: Sarah goes jogging every 4 days, and her friend goes jogging every 6 days. If they both went jogging today, in how many days will they jog together again?
Problem 3:
Question: Three traffic lights at an intersection blink at intervals of 20, 25, and 30 seconds, respectively. If they blink together at 1:00 PM, when will they all blink together again?
Problem 4:
Question: A drummer hits his drum every 2 seconds, while a guitarist strums every 3 seconds. If they both start playing at the same time, after how many seconds will they both hit their instruments simultaneously?
Problem 5:
Question: Two kids are skipping rope, one at intervals of 5 minutes and the other at intervals of 7 minutes. If they both start skipping together at 9:00 AM, when will they skip together again?
GREATEST COMMON FACTOR (GCF)
Problem 6:
Question: A teacher wants to arrange 24 pencils and 36 erasers into the largest possible groups with the same number of pencils and erasers in each group. How many groups can the teacher make?
Problem 7:
Question: Two friends have 32 and 48 marbles, respectively. They want to distribute their marbles equally into as many groups as possible. What is the largest number of groups they can make?
Problem 8:
Question: A farmer has 60 apples and 75 oranges. He wants to divide them into the largest possible equal groups without mixing apples and oranges. How many apples and oranges will be in each group?
Problem 9:
Question: A bakery has 42 chocolate chip cookies and 56 oatmeal cookies. The baker wants to package them into boxes containing the same number of each type of cookie. What is the largest number of boxes that can be made?
Problem 10:
Question: A landscaper has 90 roses and 126 tulips. He wants to plant them in rows with the same number of flowers in each row. What is the maximum number of rows he can create?
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