The H.C.F. (highest common factor) is the greatest number dividing all given numbers; the L.C.M. (least common multiple) is the smallest number divisible by all of them.
1Relations
H.C.F. × L.C.M. = product of the two numbers
H.C.F. of fractions = H.C.F. of numerators / L.C.M. of denominators
L.C.M. of fractions = L.C.M. of numerators / H.C.F. of denominators
2Remainder problems
Greatest number dividing a, b, c leaving the same remainder = H.C.F. of (b − a), (c − b), (c − a)
Least number which leaves remainder r when divided by x, y, z = L.C.M.(x, y, z) + r
Events repeating every x, y, z units coincide every L.C.M.(x, y, z)