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When is it required to find the LCM of numbers?
Solution:
Applications of LCM
The lcm is the "lowest common denominator" (lcd) that can be used before fractions can be added, subtracted or compared. The lcm of more than two integers is also well-defined: it is the smallest positive integer that is divisible by each of them. The LCM is important when adding, subtracting or comparing fractions that have different denominators. For example, you want to add $\frac{1}{2} \ to \ \frac{1}{3}$. If you know that the LCM of 2 and 3 is in fact 6 then you can say that really $\frac{1}{2} \ is \ \frac{3}{6}$ and that $\frac{1}{3}$ is really $\frac{2}{6}$. That makes the addition of fractions easy.
Whenever the question is related to classification or distribution into groups, then in all such cases it is HCF only. Whenever the question talks about the smallest or minimum, then in most cases it will be a question of LCM.
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