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 18.1 Know Your Numbers 18.2 Order of Operations 18.3 Odd and Even Numbers 18.4 The Positive, the Negative, and the Ugly 18.5 Divisibility and Remainders 18.6 Factors 18.7 Multiples 18.8 Know Your Fractions

 18.9 Decimals 18.10 Percents 18.11 Ratios 18.12 Exponents 18.13 Roots and Radicals 18.14 Sequences 18.15 Sets
Multiples
A multiple is an integer that can divide evenly into another integer. If c /d is an integer, then c is a multiple of d. The numbers 45, 27, and 18, for example, are all multiples of 9. Here’s a better example: What are some multiples of 4? The numbers 12, 20, and 96 are all multiples of 4. How do we know? Because
Also, note that any integer, n, is a multiple of 1 and n, because 1 × n = n.
Least Common Multiple
The least common multiple (LCM) of two integers is the smallest multiple that the two numbers have in common. The LCM of two numbers is, like the GCF, useful when manipulating fractions. Also similar to the GCF, you can’t find the LCM without using prime factorization. For example, what’s the least common multiple of 4 and 6? Begin by prime factorizing:
The LCM—get this, it’s tricky—is equal to the multiplication of each factor by the maximum number of times it appears in either number. Since 2 appears twice in the prime factorization of 4, it will appear twice (2 × 2) in the LCM. Since 3 appears once, it will appear once. So the LCM of 4 and 6 is 2 × 2 × 3 = 12.
One more example will help. What is the LCM of 14 and 38? Prime factorize:
Since 2 appears a maximum of once in either number, it will appear once in the LCM. Same goes for 7 and 19, making the LCM 2 × 7 × 19 = 266.
 Jump to a New ChapterIntroductionThe Discipline of DisciplineSAT StrategiesThe SAT Personal TrainerMeet the Writing SectionBeat the EssayBeat Improving SentencesBeat Identifying Sentence ErrorsBeat Improving ParagraphsMeet the Critical Reading sectionBeat Sentence CompletionsReading Passages: The Long and Short of ItThe Long of ItThe Short of ItSAT VocabularyMeet the Math SectionBeat Multiple-Choice and Grid-InsNumbers and OperationsAlgebraGeometryData, Statistics, and Probability
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