Module 3 · Number System
Chapter 30: Multiples
Number System
2 topics
What this chapter covers
The 2 topics below make up Multiples on the CAT. Click any topic to open its notes, examples and practice test.
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Formula Reference Sheet
This chapter
Counting in a range
| Multiples of k in [1, N] | floor(N / k) |
|---|---|
| Multiples of k in [A, B] | floor(B/k) − floor((A−1)/k) |
| Common multiples of a, b in [1, N] | floor(N / LCM(a, b)) |
| kth common multiple of a, b | k × LCM(a, b) |
| nth multiple of k | n × k |
Inclusion–exclusion (divisibility)
| Divisible by a OR b | floor(N/a) + floor(N/b) − floor(N/LCM(a,b)) |
|---|---|
| Divisible by a AND b | floor(N / LCM(a, b)) |
| Divisible by NEITHER a nor b | N − [floor(N/a) + floor(N/b) − floor(N/LCM)] |
| Three sets a, b, c (OR) | Σfloor(N/x) − Σfloor(N/LCM pairs) + floor(N/LCM(a,b,c)) |
| Exactly one of a, b | [floor(N/a) − floor(N/LCM)] + [floor(N/b) − floor(N/LCM)] |
CAT reference
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