Write the LCM of the following pairs of numbers:
1) 8 and 12 2) 3 and 15
3) 7 and 11 4) 9 and 10
5) 24 and 36 6) 20 and 25
7) 42 and 14 8) 30 and 12
14) a. A restaurant is open 24 hours per day. The manager wants to divide the day into work shifts of equal length. The shifts should not overlap, and all shift durations should be a whole number of hours. Describe the different ways this can be done.
b. This restaurant's two neon signs are turned on at the same time. Both signs blink as they are turned on. One sign blinks every 9 seconds. The other sign blinks every 15 seconds. In how many seconds will they blink together again?
Write the GCF of the following pairs of numbers:
16) 18 and 30 17) 9 and 25
18) 60 and 45 19) 23 and 29
20) 49 and 14 21) 140 and 25
22) 142 and 148 23) 84 and 105
27) Mr. Mendoza and his 23 students are planning to have hot dogs at their class picnic. Mr. Mendoza can buy hot dogs in packages of 12 and buns in packages of 8.
a. Mr. Mendoza plans that everyone will get the same number of hot dogs and buns and there will be no leftovers. What are the least number of hot dogs packages and the least number of bun packages Mr. Mendoza can buy? How many hot dogs and buns will each person get?
b. Suppose that the class invites the principal, the secretary, the bus driver, and three parents to help supervise. How many packages of hot dogs and buns will Mr. Mendoza need to buy so everyone will get the same number of hot dogs and buns with no leftovers? How many hot dogs and buns will each person get?
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