# How to find the hcf and lcm?

1. Homework Statement
This is slightly embarassing, but how do you find the hcf and lcm?
For example, 22,24,30. What would the hcf and lcm be?
Or,
The period of f(x)=sinx+cosx is the lcm of 2pi, 2pi, what would that be?

2. Homework Equations

HCF*LCM=f(x)*g(x)

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Tom Mattson
Staff Emeritus
Gold Member
I know what an LCM is, but what's an HCF? Did you perhaps mean GCF?

HallsofIvy
Homework Helper
Perhaps that was "Highest" Common Factor. A friend of mine who is not "mathematically" inclined suggested I say "smallest common factor" rather than "least common factor". She said that always made her wonder- what factor is "least common"!

Chaoseverlasting, in an attempt to reduce some of the chaos, remember that "Least Common Multiple" means the smallest number that is a multiple of each. For example, the least common multiple of 6 and 4 is 12: 12 is 2(6) and 3(4)- it is a multiple of both and is the smallest number that has that property. The least common multiple of 6 and 3, on the other hand, is just 6: 6= 2(3) and 1(6).

Now, in general, what is the least common multiple of any number, a, and itself. What is the "greatest (or highest) common factor"- that is a number such that each of the given numbers is a multiple of IT- if both numbers are equal?

Thanks, that helped.

for HCF I guess you mean highest common factor, which is usually called the GCD, Greatest Common Divisor.

let's say you want to find GCD of 45 and 12, then
GCD(45,12)=GCD(45-12,12)=GCD(45-12-12-12,12)=GCD(9,12)=GCD(9,12-9)=GCD(9,3)=GCD(9-3-3-3,3)=GCD(0,3)

obviously, GCD(45,12)=GCD(0,3)=3

now, for lcm,
LCM(a,b)=a*b/GCD(a,b)

In the UK, HCF is what we use for what in the US you term GCD or GCF.