ماشین‌حساب ب.م.م و ک.م.م
ب.م.م ۱۶ و ۲۴ برابر ۸ است. این ماشین‌حساب بزرگ‌ترین مقسوم‌علیه مشترک و کوچک‌ترین مضرب مشترک دو یا چند عدد طبیعی را همراه با تجزیه به عوامل اول پیدا می‌کند.
نتیجه
مقادیر را وارد کنید و برای دیدن نتیجه «محاسبه» را بزنید.
فرمول
For two numbers, the GCD and LCM multiply to the product of the numbers.
نحوه استفاده از این ماشین‌حساب
- Type the numbers, e.g. 12, 18, 30.
- Press Calculate to see the GCD, the LCM and each number’s prime factorisation.
مثال‌های حل‌شده
GCD and LCM of 12 and 18
12 = 2² × 3 and 18 = 2 × 3².
GCD takes the lowest powers: 2 × 3 = 6. LCM takes the highest: 2² × 3² = 36.
The GCF of 16 and 24
16 = 2⁴ and 24 = 2³ × 3. The greatest common factor takes the shared primes at their lowest power: 2³ = 8.
The LCM takes every prime at its highest power: 2⁴ × 3 = 48.
Check: 8 × 48 = 384 = 16 × 24.
The GCF of 16 and 36
16 = 2⁴ and 36 = 2² × 3². The only shared prime is 2, at power 2: GCF = 4.
LCM = 2⁴ × 3² = 144. Check: 4 × 144 = 576 = 16 × 36.
اشتباه‌های رایج
- Mixing up GCF and LCM: the GCF is never bigger than the smallest number; the LCM is never smaller than the largest.
- Using the highest power for the GCF: for 16 = 2⁴ and 24 = 2³ × 3 the GCF uses 2³, not 2⁴.
- Stopping at a common factor that isn’t the greatest: 4 divides 16 and 24, but 8 is bigger.
پرسش‌های متداول
What is the GCF of 9 and 36?
9, because 9 divides 36 exactly (36 = 4 × 9). When one number divides the other, it is the GCF.
Are GCF, GCD and HCF the same?
Yes — greatest common factor (GCF), greatest common divisor (GCD) and highest common factor (HCF, the usual UK name) all mean the same number.
Is GCD the same as HCF or GCF?
Yes. Greatest common divisor, highest common factor and greatest common factor all mean the same thing.
Where is the LCM used?
Adding fractions uses the LCM of the denominators — the least common denominator.