What Does LCM Mean in Mathematics?

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For a given set of numbers, the least common multiple (LCM) is the smallest number each divides into with no remainder.

Like Comparison

When presented with fractions of differing denominators, finding the LCM will allow you to compare like terms. For example, 3/8 and 5/12 are fractions with similar values and different terms. To find the LCM, express each denominator as a product of prime number powers.

2^3 = (2 × 2 × 2) = 8 \text{ and } 2^2 × 3^1 = (2 × 2) × 3 =12

Multiply the highest power of each prime factor to find the LCM.

2^3 × 3^1=24

With this,

\frac{3}{8} \text{ becomes } \frac{9}{24} \text{ and } \frac{5}{12} \text{ becomes } \frac{10}{24}

presenting a clearer numerical comparison.

Common Multiple

Another way to find the LCM is to simply find any common multiple, then divide by prime factors to find the smallest multiple. For 24 and 26 we find

624 = 24 × 26 \\24=2^3 × 3 \text{ and } 26=2 × 13

By dividing 624 by 2, the only common prime factor, we get 312 as an LCM.

Practical Use

Like terms are important for any quantified comparison. Different quantities of different goods are shipped on identical vehicles because vehicles are built to carry many unique objects. Ships are an LCM for overseas bulk transport, just as an economy car is the LCM for localized human transport.

Watch the video below for an example on how to find LCM as well as GCF using the Ladder Method:

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