🔢 LCM & GCF Calculator

GCF(a, b):
while b ≠ 0:
temp = b
b = a mod b
a = temp
return a

Example: GCF(48, 18)
48 mod 18 = 12 → GCF(18, 12)
18 mod 12 = 6 → GCF(12, 6)
12 mod 6 = 0 → GCF = 6

LCM(a, b) = |a × b| / GCF(a, b)

Example: LCM(12, 18)
GCF(12, 18) = 6
LCM = (12 × 18) / 6 = 216 / 6 = 36

GCF = product of COMMON prime factors (lowest powers)
LCM = product of ALL prime factors (highest powers)

Example: 12 = 2² × 3 18 = 2 × 3²

GCF = 2¹ × 3¹ = 6 (min of each power)
LCM = 2² × 3² = 36 (max of each power)

GCF(a,b,c) = GCF(GCF(a,b), c)
LCM(a,b,c) = LCM(LCM(a,b), c)

Example: GCF(8, 12, 20)
GCF(8,12) = 4, then GCF(4,20) = 4

LCM: When do two repeating events coincide?
→ Bus A every 12 min, Bus B every 18 min
→ LCM(12,18) = 36 min → meet every 36 min

GCF: Largest equal pieces you can cut?
→ 48cm and 18cm ribbons → GCF=6 → 6cm pieces
→ Fractions: simplify 12/18 → divide by GCF(12,18)=6 → 2/3