Marie wishes to plant pumpkins and sunflowers, so this morning she bought packs of seeds at a local gardening shop. Pumpkin seeds were sold in packages of 11 seeds, while sunflower seeds were sold in packs of 12. If Marie bought the same number of each type of seed, what is the smallest number of pumpkin seeds she must have bought?
Question
Marie wishes to plant pumpkins and sunflowers, so this morning she bought packs of seeds at a local gardening shop. Pumpkin seeds were sold in packages of 11 seeds, while sunflower seeds were sold in packs of 12. If Marie bought the same number of each type of seed, what is the smallest number of pumpkin seeds she must have bought?
Solution
To solve this problem, we need to find the least common multiple (LCM) of 11 and 12, because Marie bought the same number of each type of seed.
Step 1: List the multiples of each number. Multiples of 11: 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132... Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132...
Step 2: Find the least common multiple. The smallest number that appears in both lists is 132.
So, the smallest number of pumpkin seeds Marie must have bought is 132.
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