Find the least common multiple (LCM) and greatest common factor (GCF) of two numbers, plus the ratio between them simplified to its lowest terms.
The greatest common factor (GCF) is the largest number that divides both numbers evenly. For 12 and 18, the GCF is 6, since 6 is the highest number that divides both 12 and 18 evenly. The least common multiple (LCM) is the smallest number that both numbers divide into. For 12 and 18, the LCM is 36.
A concrete example: if you're adding the fractions 1/12 and 1/18, you need a common denominator — and the smallest possible common denominator is exactly the LCM of 12 and 18, i.e. 36. If instead you want to simplify a fraction like 12/18, you divide the numerator and denominator by the GCF (6), giving 2/3.
LCM is used, among other things, to find a common denominator when adding or subtracting fractions with different denominators. It's also used to figure out when two events that happen at regular intervals will coincide.
GCF (greatest common factor) is the largest number that divides both numbers evenly, and is used to simplify fractions. LCM (least common multiple) is the smallest number that both numbers divide into, and is used to find common denominators.
GCF is used to simplify a fraction to its lowest terms, by dividing the numerator and denominator by the GCF. LCM is used to find the least common denominator when adding or subtracting fractions with different denominators.