How do you do LCM and HCF in maths?

Answer 1

Example: 30 and 42

Factor them.

2 x 3 x 5 = 30

2 x 3 x 7 = 42

Select the common factors.

2 x 3 = 6, the GCF

Select the highest amount of each factor.

2 x 3 x 5 x 7 = 210, the LCM

Check it.

30 x 42 = 1260

210 x 6 = 1260

It checks.

Answer 2

Euclid's Algorithm is a fast way to get the greatest common factor: http://en.wikipedia.org/wiki/Euclidean_algorithm. You can also use prime factors, but that is slower, especially for large numbers.

For the least common multiple, use the fact that the least common multiple, multiplied by the greatest common factor, is equal to the product of the two numbers. In other words, since (by Euclid's Algorithm) the greatest common factor of 20 and 30 is 10, you calculate 20 x 30 / 10, to get the least common multiple, which in this case is 60.