lcm
Master LCM
Learn the secrets of rapid mental computation used in competitive exams. These strategies will help you bypass traditional paper-and-pencil methods.
➕ Addition ➖ Subtraction ✖️ Multiplication ➗ Division x² Squaring xⁿ Exponentiation √ nth Root % Percentage △ Pythagorean Triples lcm LCM hcf HCF
lcm
★ LCM via listing multiples
List multiples of both numbers until you find the first common one. Fast for small numbers.
Example
LCM(4,6): 4,8,12 and 6,12 → LCM = 12 lcm
★ LCM = (a × b) ÷ GCD
The fastest formula: multiply the two numbers, then divide by their GCD.
Example
LCM(8,12): GCD=4. 8×12=96. 96÷4 = 24 lcm
★ Prime factorisation method
Break both numbers into prime factors. Take the highest power of each prime that appears.
Example
LCM(12,18): 12=2²×3, 18=2×3². Take 2²×3²=36 lcm
★ LCM of coprime numbers
If GCD(a,b)=1, then LCM(a,b)=a×b. Check for coprimality first to save work.
Example
LCM(7,9): GCD=1. So LCM = 7×9 = 63 lcm
★ Scaling up LCM
LCM(ka, kb) = k × LCM(a,b). Factor out the common multiplier first.
Example
LCM(10,15): factor out 5 → 5×LCM(2,3) = 5×6 = 30 🧠 Practice
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