LCM & HCF Exam Shortcuts / Tips / পৰীক্ষা টিপচ্

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Exam Shortcuts / Tips / পৰীক্ষা টিপচ্

HCF & LCM – Memory Table

Basic definitions: Methods to find HCF

(A) Prime Factorization Method

Ex: Find HCF of 36 and 60

Soln

36 = 2² × 3², 60 = 2² × 3 × 5 Common factors = 2² × 3 = 12, HCF = 12

(B) Division Method (Euclid’s method)

Ex: Find HCF of 60 and 36

Soln: ???

(C) Shortcut Trick (for 2 or 3 numbers)

Methods to find LCM

(A) Prime Factorization Method

Ex: Find LCM of 12 and 18

Soln

12 = 2² × 3, 18 = 2 × 3², LCM = 2² × 3² = 36

(B) Division Method (for 2 or more numbers)

Ex: Find LCM of 12, 18, 24

Soln: Numbers: 12, 18, 24

Divide by 2: 12 → 6, 18 → 9, 24 → 12 → New numbers: 6, 9, 12

Divide by 2 again: 6 → 3, 9 → 9, 12 → 6 → New numbers: 3, 9, 6

Divide by 3: 3 → 1, 9 → 3, 6 → 2 → New numbers: 1, 3, 2

Divide by 2: 1 → 1, 3 → 3, 2 → 1 → New numbers: 1, 3, 1

Divide by 3: 1 → 1, 3 → 1, 1 → 1 → Stop (all numbers = 1)

Multiply all divisors used: 2 × 2 × 3 × 2 × 3 = 72

LCM = 72

(C) Relation Between HCF and LCM

For any two numbers,

HCF × LCM = Product of numbers

Ex: If numbers are 12 and 18,

Soln: HCF = 6, so LCM = (12 × 18) / 6 = 36

HCF & LCM – Short Tricks & Memory Tips

      Three consecutive numbers: 10, 11, 12

LCM = 10×11×12 = 1320

       Three consecutive even numbers: 12, 14, 16

LCM = (12×14×16) ÷ 2 = 2688÷2 = 1344

       For fractions (a/b, c/d)

HCF & LCM of the same fractions:

Ex: HCF(2/3, 4/5)

HCF of numerators = HCF(2, 4) = 2

LCM of denominators = LCM(3, 5) = 15

HCF = 2/15

Ex: HCF(2/3, 4/5)

LCM of numerators = LCM(2, 4) = 4

HCF of denominators = HCF(3, 5) = 1

LCM = 4/1 = 4

Tip for fast memory:

Example Mixed Problem

Find HCF and LCM of 16a²bc³, 32abc, 64a³bc²

LCM: Take highest powers= 64a³bc³

HCF: Take lowest powers= 16abc²

HCF = 16abc² LCM = 64a³bc³

Example:Find HCF of 36 and 60