Each of these problems is solved by finding a least common multiple (LCM). In some, two things repeat and you find when they next line up; in others, one amount is shared into equal groups and you find the smallest amount that fits. Read carefully, then find the smallest number that works.
A teacher has a box of pencils. Shared equally among 3 students, exactly 2 are left over; among 6 students, exactly 2 are left over; and among 4 students, exactly 2 are left over. If every student always gets at least one pencil, what is the smallest number of pencils in the box?
A teacher has a box of pencils. Shared equally among 3 students, exactly 2 are left over; among 4 students, exactly 2 are left over; and among 6 students, exactly 2 are left over. If every student always gets at least one pencil, what is the smallest number of pencils in the box?
Mia has a jar of marbles. Shared equally among 6 friends, exactly one is left over; among 5 friends, exactly one is left over; and among 3 friends, exactly one is left over too. If every friend always gets at least one marble, what is the smallest number of marbles in the jar?
A florist buys roses in bunches of 8 and tulips in bunches of 12. She wants a bouquet with the same number of roses as tulips, using whole bunches only. What is the smallest number of each flower the bouquet can have?
In the school band, one drummer strikes a cymbal every 8 beats, and another strikes a cowbell every 6 beats. They just struck at the same time. After how many beats will they strike together again?
Veggie patties come in packs of 12 and buns come in packs of 9. What is the smallest number of each you can buy so that every patty gets exactly one bun, with none left over?