Math and Arithmetic

Factoring and Multiples

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There are no greatest common multiples only greatest common factors

When doing fractions it is the greatest common factor (GCF) and the least common multiple (LCM). You want the GCF when you are reducing fractions to their simplest form. When changing the denominators to a common one, you want the LCM.

Finding the greatest common factor helps when you are reducing fractions.

The GCF helps in simplifying fractions and the LCM helps in adding and subtracting them.

When adding or subtracting fractions with different denominators

Use the LCM when you are adding and subtracting unlike fractions. Use the GCF when you are simplifying fractions.

Factors are useful when you're trying to reduce fractions. Multiples are useful when you're trying to find a least common denominator.

One common application of greatest common factors is to simplify fractions. Note that you don't necessarily need the GREATEST common factor; you can simplify by dividing both numbers by any common factor, and then continue looking for additional factors.

The greatest common multiple of any set of integers is infinite.

The Greatest Common Factor (GCF) is: 41The Least Common Multiple (LCM) is: 246

Factors create multiples, multiples break down into factors.

When reducing fractions to their lowest terms the HCF is used When adding or subtracting fractions with different denominators the LCM is used

The concept of factors (and common factors) is applicable to whole numbers, not to fractions. The numerator and denominator of a rational fraction are integers and they can have a greatest common factor but that is not a factor of the fraction.

There cannot be common factors, a greatest common factor, or a least common multiple because "common" refers to factors or multiples that two or more numbers have in common.

Simplification using the greatest common factor does.Simplification using the greatest common factor does.Simplification using the greatest common factor does.Simplification using the greatest common factor does.

Any set of factors that had 18 as a common multiple would also have multiples of 18 in common, so 18 can't be greatest. 9 and 6 have 18 as their least common multiple.

Any number can be a common multiple of two or more fractions. The concept of common multiples is useful only in the context of multiples of integers.

Common factors go into the numbers, the numbers go into common multiples.

Common factors: 1 and 2 Common multiples: Any multiple of 132

Factors go into numbers, numbers go into multiples.

28 multiples are 7,4,1,2,14,28, 63 multiples are 1.63.3.3.7 greatest is 7

you have to compare the common fractions

You may have answered your own question. Equivalent fractions have common factors. If they don't have common factors, they aren't equivalent.

You need to have 2 numbers to work out the common multiples...The whole idea of common multiples is that they are multiples which both numbers share (or have in common).Also, the GREATEST multiple of anything is infinity

For practical purposes, there are greatest common factors and least common multiples. The greatest common multiple of any set of integers is infinite.

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