4 min read
2026-02-25
These techniques will help you find GCD and LCM even without a calculator.
Check divisibility sequentially: by 2, by 3, by 5, by 7. For most problems, this is sufficient.
By 2: the last digit is even
By 3: the sum of digits is divisible by 3
By 5: ends in 0 or 5
By 9: the sum of digits is divisible by 9
By 4: the last two digits are divisible by 4
Factor both numbers into primes. The GCD is the product of common factors; the LCM is the product of all factors at their highest powers.
If two numbers are coprime (share no common divisors other than 1), their GCD = 1 and their LCM = their product.
When adding fractions, the common denominator is the LCM of the denominators. Don't just take the product — the LCM is often smaller.
The GCD cannot be larger than the smaller of the numbers. The LCM cannot be smaller than the larger of the numbers. Use these constraints for verification.
GCD(a, b, c) = GCD(GCD(a, b), c). Calculate sequentially for pairs — it's simpler than working with three numbers at once.
See also: Fraction Calculator, Prime Number Checker, Roman Numerals