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Prime Factor Alignment Table

NumberUnique FactorsCommon Shared Factors
Pack A (a = 12)
2
23
Pack B (b = 18)
3
GCD (Max Bag Size)6
LCM (Min Fruits to Match)36

Variable Adjuster

Fruit Pack A Size (a)12
260
Fruit Pack B Size (b)18
260

Greatest Common Divisor & Least Common Multiple

GCD & LCM

The Greatest Common Divisor (GCD) is the largest positive integer that divides both numbers. The Least Common Multiple (LCM) is the smallest positive integer that is divisible by both numbers.

GCD(a,b)⋅LCM(a,b)=a⋅b\text{GCD}(a, b) \cdot \text{LCM}(a, b) = a \cdot b

Whiteboard Solver Steps

Step 1

Prime Factorisation of Fruit Pack A Size (12)

Decompose the size of Fruit Pack A (a=12a = 12) into its prime factor representation.

12=2×2×312 = 2 \times 2 \times 3
Step 2

Prime Factorisation of Fruit Pack B Size (18)

Decompose the size of Fruit Pack B (b=18b = 18) into its prime factor representation.

18=2×3×318 = 2 \times 3 \times 3
Step 3

Find Greatest Common Divisor (GCD / HCF)

Identify all prime factors that both fruit packs share. The product of these common factors gives the GCD. This represents the maximum size of identical bags we can partition both fruit packs into without any leftovers.

GCD(12,18)=2×3=6\text{GCD}(12, 18) = 2 \times 3 = 6
Step 4

Find Least Common Multiple (LCM)

Find the least common multiple of both pack sizes. This represents the minimum total number of fruits of each type we need to purchase to get equal quantities of both types while only buying complete packs.

LCM(12,18)=12×18GCD(12,18)=36\text{LCM}(12, 18) = \frac{12 \times 18}{\text{GCD}(12, 18)} = 36