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.
Factor (Number)
A factor is an integer that divides another integer perfectly without leaving a remainder. On the Digital SAT, factors appear frequently in Math Modules 1 and 2, often within algebraic simplification or polynomial questions. Typically, students must identify factors to find roots or simplify expressions, making this concept vital for a high score.
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.
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.
Sequence
A sequence is an ordered list of numbers following a specific rule. On the Digital SAT, sequences appear in the Math section, typically within Advanced Math. These questions occur approximately once or twice per test, requiring students to identify patterns or calculate specific terms using arithmetic or geometric formulas.
A multiple on the SAT is a number that can be divided by another number without leaving a remainder. In the context of the Digital SAT, multiples are fundamental to solving problems involving frequency, common denominators, and sequences. Understanding multiples allows students to navigate questions in the Math section that involve finding the Least Common Multiple (LCM) to synchronize different rates or cycles effectively.
You identify a multiple by determining if a number can be expressed as the product of a specific integer and another integer. For instance, to check if 24 is a multiple of 8, you divide 24 by 8; since the result is exactly 3 with no remainder, 24 is a multiple. On the SAT, use the built-in calculator to quickly verify divisibility for larger numbers in complex word problems.
The difference between a multiple and a factor lies in their relationship to a base number. A factor is a number that divides into another number evenly (e.g., factors of 12 are 1, 2, 3, 4, 6, 12), whereas a multiple is the result of multiplying that base number by an integer (e.g., multiples of 12 are 12, 24, 36). Factors are generally smaller or equal to the number; multiples are larger or equal.
Approximately 5% to 10% of the Math section questions involve multiples directly or indirectly. While few questions ask 'What is a multiple?' explicitly, many require the concept to solve problems regarding time intervals, overlapping patterns, or algebraic simplification. They typically appear in both easy and hard modules, with more complex applications involving variables appearing in the second, adaptive module of the Digital SAT.
