Quick Answer
A multiple is the product of any integer and another integer. On the Digital SAT, multiples appear frequently in Math Modules 1 and 2, often within word problems involving cycles or sequences. Typically, students must calculate the Least Common Multiple (LCM) to solve problems concerning synchronized events or common denominators.
A multiple of an integer $n$ is a number $m$ that can be expressed as $m = n \times k$, where $k$ is an integer. In simpler terms, a multiple is any number that can be divided by $n$ with a remainder of zero.
Question: A blue light flashes every 8 seconds and a red light flashes every 12 seconds. If they both flash at the same time, how many seconds will pass before they next flash together? \n\nSolution: This requires the Least Common Multiple (LCM) of 8 and 12. \nMultiples of 8: 8, 16, 24, 32... \nMultiples of 12: 12, 24, 36... \nThe smallest common multiple is 24. They will flash together in 24 seconds.
Mistake 1: Confusing multiples with factors, leading students to provide a smaller divisor rather than a larger product.
Mistake 2: Forgetting that zero is technically a multiple of every integer, though SAT questions usually specify 'positive integers'.
Mistake 3: Simply multiplying two numbers to find a common multiple instead of finding the 'least' common multiple, which can lead to unnecessarily large calculations.
Students targeting 750+ should know that the product of two numbers divided by their Greatest Common Factor (GCF) always equals their Least Common Multiple (LCM). This formula, $LCM(a, b) = (a \times b) / GCF(a, b)$, is a powerful shortcut for handling large numbers in the advanced sections of Math Module 2.
Integer
An integer is a whole number that can be positive, negative, or zero. On the Digital SAT, integers appear frequently across both Math modules, particularly in student-produced response questions where answers must often be non-decimal. Mastering integers is essential for solving approximately 15-20% of algebraic and data analysis problems.
Prime Number
A prime number is a positive integer greater than 1 with exactly two distinct factors: 1 and itself. On the Digital SAT, prime numbers frequently appear in Math Module 1 and 2 within Number Properties or Algebra questions. Students typically encounter at least one question involving prime factorization or integer constraints per test.
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Remainder
A remainder is the integer value left over after dividing one number by another. On the Digital SAT, remainders appear in Math Modules 1 and 2, often within word problems or polynomial algebra. This concept is tested in approximately 2-4% of math questions, requiring students to interpret leftovers in real-world contexts.