Find the LCM of the following numbers

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In summary, the conversation discusses the process of finding the lowest common multiple (lcm) using the given options. After some initial incorrect thinking, it is determined that the correct way is to first find the product and then divide by the highest common factor. The resulting lcm is ##2^5 \cdot 3 \cdot 11^2 \cdot 23 = 267168##.
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chwala
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lcm
This is the problem, i think its not possible to get the lcm from the options given, i need a second opinion on this:

1632223863171.png
lcm ought to be## 22×23×48=24,288##

lcm[{22, 23, 32, 33}]=24,288## ok my initial thinking here was not correct. I was finding the lcm without first finding the product...

The correct way is to simply find lcm ##(726, 736)=267,168##
 
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  • #2
It ought to be ##2^5 \cdot 3 \cdot 11^2 \cdot 23 = 267168##
 
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  • #3
ergospherical said:
It ought to be ##2^5 \cdot 3 \cdot 11^2 \cdot 23 = 267168##
really?
 
  • #4
ergospherical said:
It ought to be ##2^5 \cdot 3 \cdot 11^2 \cdot 23 = 267168##
ok, you had to find the product first...cheers...
 
  • #5
The highest common factor is only ##2##. So, the lowest common multiple must be half the product.
 
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FAQ: Find the LCM of the following numbers

What is the LCM and why is it important?

The LCM (Least Common Multiple) is the smallest positive integer that is divisible by all of the given numbers. It is important because it helps us find the smallest common multiple of a set of numbers, which is useful in solving problems involving fractions, ratios, and proportions.

How do you find the LCM of two numbers?

To find the LCM of two numbers, you can use the prime factorization method. First, find the prime factors of each number. Then, write out the prime factors of each number in a vertical list and include the highest power of each common factor. Finally, multiply all the numbers in the list to get the LCM.

Can the LCM of two numbers be smaller than either of the numbers?

No, the LCM of two numbers cannot be smaller than either of the numbers. This is because the LCM must be a multiple of both numbers, so it must be at least as large as the larger number.

What is the difference between LCM and GCD?

The LCM (Least Common Multiple) is the smallest positive integer that is divisible by all of the given numbers. On the other hand, the GCD (Greatest Common Divisor) is the largest positive integer that divides evenly into all of the given numbers. In other words, the LCM is the smallest number that all the given numbers can divide into, while the GCD is the largest number that can divide all the given numbers.

How is the LCM used in real-life situations?

The LCM is used in various real-life situations, such as finding the best time to schedule recurring events, calculating the amount of materials needed for a project, and solving problems involving fractions, ratios, and proportions. It is also used in programming and computer science to optimize algorithms and find the most efficient way to complete a task.

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