HCF and LCM of Fractions

• LCM of fractions = LCM(numerators) / HCF(denominators)
• HCF of fractions = HCF(numerators) / LCM(denominators)

Why it works: Prime factorization exposes exactly which prime “building blocks” and how many of each are shared. The common part (lowest shared power) is what every number can be divided by — that is HCF. The full set of blocks needed to be divisible by every number (highest power appearing anywhere) is the LCM. The HCF×LCM=a×b identity is a direct algebraic consequence of writing HCF = product of min powers and LCM = product of max powers, since min(x,y) + max(x,y) = x + y for corresponding exponents.