grade E. 4 GCF and LCM: word problems COV
Valentina plants trees in rowis of 45 while her friend, Diana, plants trees in rows of 29. If both
friends have the same number of trees to plant, what is the smallest number that each will
have to plant?
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To determine the smallest number of trees Valentina and Diana will need to plant, we find the least common multiple (LCM) of their rows: 45 and 29. The LCM is the smallest multiple that both numbers share. Since 45 is a multiple of 5 and 9, and 29 is a prime number, the LCM is simply 45 multiplied by 29, which is 1,305. Therefore, the smallest number of trees each will have to plant is 1,305.

Now, here’s a fun fact: The process of finding the LCM can actually be compared to planning a synchronized dance routine! Just like how dancers need to find common beats to move together, we look for common multiples to ensure both friends can plant their trees in harmony.

And if you’re curious about the GCF (greatest common factor), you can find it using prime factorization or the Euclidean algorithm, which states that the GCF of two numbers can be obtained by repeatedly replacing the larger number by its remainder when divided by the smaller number. This method can save you time and is a great way to show off your math skills!