The lowest common multiple (LCM) of two or more numbers is the smallest number that is a multiple of all of them.
Method 1 — list multiples: Multiples of 4: 4, 8, 12, 16, 20, … Multiples of 6: 6, 12, 18, 24, … LCM = 12
Method 2 — prime factor decomposition: $$4 = 2^2 \qquad 6 = 2 \times 3$$ Multiply shared and unshared prime factors using the highest power of each: $$\text{LCM}(4, 6) = 2^2 \times 3 = 12$$
Using a Venn diagram: place prime factors of each number in a Venn diagram — the LCM is the product of all factors in the diagram (including the intersection).
Why it matters: used to find a common denominator when adding or subtracting fractions.
Common error: confusing LCM with HCF — LCM is always greater than or equal to the numbers, HCF is always less than or equal.