The Least Common Multiple (LCM) of 108 and 144 is 432. LCM is a fundamental concept in Mathematics, sometimes referred to as the LCD (Least Common Denominator). For a more in-depth understanding of LCM and its counterpart, HCF (Highest Common Factor), students may find this HCF and LCM article useful. This resource can help students enhance their problem-solving skills and logical thinking abilities, ultimately leading to better exam scores. In this article, we will be focusing on how to efficiently compute the LCM of 108 and 144.
LCM of 108 and 144 - Calculation Methods, Examples and FAQs
Last Updated on Jun 10, 2024
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Understanding the LCM of 108 and 144
The LCM of 108 and 144 is 432.
Determining the LCM of 108 and 144
There are several ways to find the LCM of 108 and 144, including:
- Prime Factorisation
- Division Method
- Listing the Multiples
Using Prime Factorisation to Find the LCM of 108 and 144
With the Prime Factorisation method, we can express the numbers 108 and 144 as the product of their prime factors. In this case, 108 and 144 can be expressed as follows:
108 = 2 × 2 × 3 × 3 × 3
144 = 2 × 2 × 2 × 2 × 3 × 3
Thus, LCM (108, 144) = 2 × 2 × 2 × 2 × 3 × 3 × 3 = 432
Using Division Method to Find the LCM of 108 and 144
The Division Method involves dividing the numbers 108 and 144 by their prime factors until we get the result as one in the complete row. The product of these divisors gives the least common multiple of 108 and 144.
After the division process is complete, we find that the LCM (108, 144) = 2 × 2 × 2 × 2 × 3 × 3 × 3 = 432
Using the Listing Multiples Method to Find the LCM of 108 and 144
This method involves listing out the multiples of the given natural numbers until we find the lowest common multiple among them. The following table shows the multiples of 108 and 144.
As we can see, the LCM (108, 144) = 432
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Frequently Asked Questions
What is the LCM of 108 and 144?
The LCM of 108 and 144 is 432.
What is the difference between the LCM of 108 and 144 and the HCF of 108 and 144?
The LCM of 108 and 144 is 432 and the HCF of 108 and 144 is 36.
Is 56 the greatest common factor of 108 and 144?
No. The greatest common factor of 108 and 144 is 36.
If the LCM of 108 and 144 is 432. Calculate the GCF.
GCF × LCM = 108 × 144, Given LCM = 432, GCF × 432 = 108 × 144, GCF = 36.
Mention the relation between GCF and LCM of 108 and 144.
The relation between GCF and LCM of 108 and 144 is GCF × LCM = 108 × 144, GCF × LCM = 15552.
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