difference between hcf and lcm

HCF = Highest Common Factor

LCM = Lowest Common Multiple

A factor is a number than goes into another number x amounts of times, e.g. 2 is a factor of 10, it goes into 10 5 times (5 being the x)

3 is a factor of 36, it goes in 12 times etc.

A multiple is a what is says, a multiple. 12 is a multiple of 3 because 3*4=12, 12 as also a multiple of 1,2 and 6, so you can say that 12 has the factors of 1,2,3,4 and 6.

To find the HCF of a pair of numbers you need to break down the numbers into their PRIME factors (all numbers are a multiple of an arrangement of primes) and then find those in common and multiply them together.

E.g.

HCF of 78 and 104

78 = 2*3*13

104 = 2*4*13

The common numbers are 2 and 13, so the HCF is 2*13=26

The LCM is found, again by breaking the numbers down into their prime factors and multiplying each number WITH THE LARGEST EXPONENT. Let me explain.

I will make this a little harder by finding the LCM of 3 numbers.

E.g.

32 = 2*2*2*2*2 = 2^5

72 = 2*2*2*3*3 = 2^3*3^2

318 = 2*3*53

So, any number without an exponent is equal to that number raised the the first power.

We see that 32 clearly has the most 2s, so we start with 2^5 (we ignore the 2^2 and the 2^1 in the other two numbers because they have a smaller exponent) we then multiply that by 3^2, (ignoring the 3 in 318 because, again, it has a smalled exponent) finally we need to multiply this by 53, there are no other numbers with 53 as a factor so 53^1 is the highest exponent.

Right, so we have 2^5*3^2*53 = 15,264

And that's the lowest common multiple, the lowest number (closest to zero) that all 3 numbers, 32,72 and 318, go into or are factors of.

I hope this helps.