Module 3 · Number System
Chapter 33: LCM
Number System
3 topics
What this chapter covers
The 3 topics below make up LCM on the CAT. Click any topic to open its notes, examples and practice test.
Study material & tests
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Formula Reference Sheet
This chapter
Core LCM & HCF
| LCM by factorisation | LCM = product of each prime to its HIGHEST power |
|---|---|
| HCF by factorisation | HCF = product of each common prime to its LOWEST power |
| HCF–LCM identity (two numbers) | HCF(a,b) × LCM(a,b) = a × b |
| Missing LCM | LCM = (a × b) / HCF |
| Missing number | b = (HCF × LCM) / a |
Fractions & applications
| LCM of fractions | LCM(numerators) / HCF(denominators) |
|---|---|
| HCF of fractions | HCF(numerators) / LCM(denominators) |
| Bells ring together | gap = LCM of the individual intervals |
| Least number, same remainder r | N = LCM(divisors) × k + r |
| Least number, exactly divisible | N = LCM(divisors) (the case r = 0) |
CAT reference
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