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**## Summary of the Topic

**Highest Common Factor (H.C.F.)**

If two or more algebraic expressions are given then their common factor of highest power is called the H.C.F. of the expressions.

**Least Common Multiple (L.C.M.)**

If an algebraic expression \(p\left( x \right)\) is exactly divisible by two or more expressions, then \(p\left( x \right)\)is called the Common Multiple of the given expressions. The least Common Multiple (L.C.M.) is the product of common factors togerther with non-common factors of the given expressions.

**Note:** We can find the H.C.F of given expressions by **Factorization** or by **Division**.

**Finding L.C.M. by Factorization**

After factorizing the given expressions completely, the L.C.M. is obtained by taking the product of each factor appearing in any of the given expressions, raised to the highest power with which factor appears.

**Relation between H.C.F. and L.C.M.**

- \(\text{L}\text{.C}\text{.M}\text{.}=\frac{p\left( x \right)\text{ }\!\!\times\!\!\text{ }q\left( x \right)}{\text{H}\text{.C}\text{.F}\text{.}}\) or \(\text{H}\text{.C}\text{.F}\text{.}=\frac{p\left( x \right)\text{ }\!\!\times\!\!\text{ }q\left( x \right)}{\text{L}\text{.C}\text{.M}\text{.}}\)

- \(p\left( x \right)=\frac{\text{L}\text{.C}\text{.M}\text{. }\!\!\times\!\!\text{ H}\text{.C}\text{.F}\text{.}}{q\left( x \right)}\) or \(q\left( x \right)=\frac{\text{L}\text{.C}\text{.M}\text{. }\!\!\times\!\!\text{ H}\text{.C}\text{.F}\text{.}}{p\left( x \right)}\)

Then using the formula \(\text{L}\text{.C}\text{.M}\text{.}=\frac{p\left( x \right)\text{ }\!\!\times\!\!\text{ }q\left( x \right)}{\text{H}\text{.C}\text{.F}\text{.}}\) find the L.C.M of \(p\left( x \right)\) and \(q\left( x \right)\)

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