Vijay wishes to plant pumpkins and sunflowers, so this morning he bought packs of seeds at a local gardening shop. Pumpkin seeds were sold in packages of 10 seeds, while sunflower seeds were sold in packs of 19. If Vijay bought the same number of each type of seed, what is the smallest number of pumpkin seeds he must have bought?
Question
Vijay wishes to plant pumpkins and sunflowers, so this morning he bought packs of seeds at a local gardening shop. Pumpkin seeds were sold in packages of 10 seeds, while sunflower seeds were sold in packs of 19. If Vijay bought the same number of each type of seed, what is the smallest number of pumpkin seeds he must have bought?
Solution
To solve this problem, we need to find the least common multiple (LCM) of the numbers 10 and 19, which represent the number of seeds in each pack of pumpkin and sunflower seeds, respectively. The LCM of two numbers is the smallest number that is a multiple of both numbers.
Step 1: List the multiples of each number.
Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190...
Multiples of 19: 19, 38, 57, 76, 95, 114, 133, 152, 171, 190...
Step 2: Find the smallest number that appears in both lists.
The smallest number that is a multiple of both 10 and 19 is 190.
Therefore, the smallest number of pumpkin seeds that Vijay must have bought is 190.
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