Sample Problems on LCM of 10 and 15
Problem 1: Emily is organizing her books. She has 10 books on one shelf and 15 on another. What is the least number of shelves needed if she wants to arrange them in such a way that each shelf has the same number of books?
Solution:
Emily has books on one shelf = 10
Emily has books on another shelf = 15
The LCM of 10 and 15 is 30.
Therefore, Emily needs at least 30 shelves to distribute her books equally.
Problem 2: In a school event, students are given 10 red balloons and 15 blue balloons. What is the minimum number of balloon bunches the organizers need to create if they want each bunch to have an equal number of both red and blue balloons?
Solution:
Students are given red balloons = 10
Students are given blue balloons = 15
The LCM of 10 and 15 is 30.
Hence, the organizers need to create at least 30 balloon bunches for an equal distribution.
Problem 3: Sarah practices two musical instruments. She practices one instrument every 10 days and the other every 15 days. After how many days will she need to practice both instruments on the same day?
Solution:
Sarah practices one instrument = every 10 days
Sarah practices other instrument = every 15 days.
The LCM of 10 and 15 is 30.
Therefore, Sarah will need to practice both instruments on the same day every 30 days.
Problem 4: A factory produces products in batches of 10 and 15. What is the smallest batch size they can produce if they want to manufacture the same number of products for both types of batches?
Solution:
A factory produces products in first batch size = 10
A factory produces products in second batch size = 15
The LCM of 10 and 15 is 30.
Thus, the factory should produce products in batches of 30 for an equal distribution.
Problem 5: Jason has a garden where he plants flowers in rows of 10 and trees in rows of 15. How many flowers and trees will he have in the same row after the least number of rows?
Solution:
Jason plants flowers in rows = 10
Jason plants trees in rows = 15
The LCM of 10 and 15 is 30.
Therefore, Jason will have both flowers and trees in the same row after planting 30 rows.
LCM of 10 and 15
Least Common Multiple (LCM) of 10 and 15 is 30. LCM, as the name suggests, is the smallest common multiple of all the numbers under consideration. In this article, we explore different approaches to finding the LCM of 10 and 15, such as prime factorization and listing multiples.