A calculator that can calculate both the GCF and LCM of two integers is available, but the key here is the selection of the right calculator.
The GCF calculator, also called the greatest common factor calculator, finds the largest number that divides 2 or more numbers equally without a remainder, whereas the LCM calculator finds the least common multiple of 2 or more numbers.
Step One: Do You Need the GCF or the LCM?
For simplification or division use GCF. The largest positive integer that can divide the supplied integers without leaving a remainder is known as the greatest common factor, or GCF. It aids in reducing the fraction or splitting the provided items into the greatest number so that nothing is left.
Use the LCM for two repeating events to coincide. The least common multiple is the lowest positive integer that both the numbers can divide. Suppose one event takes place after every 6 days and the other after every 8 days. Then the LCM will give us the answer for when both events will coincide.
| GCF | LCM | |
|---|---|---|
| Question it answers | What’s the biggest number that divides both? | What’s the smallest number both divide into? |
| Size | Never bigger than the smaller number | Never smaller than the bigger number |
| Fraction job | Simplifying | Finding a common denominator |
Method 1: Make Lists
It is quite effective when working with smaller numbers.
GCF of 24 and 36. Factors:
24: 1, 2, 3, 4, 6, 8, 12, 24
36: 1, 2, 3, 4, 6, 9, 12, 18, 36
The largest number that occurs in both lists is 12.
LCM of 8 and 12. Multiples:
8: 8, 16, 24, 32, 40, …
12: 12, 24, 36, 48, …
The smallest number that occurs in both lists is 24
Method 2: Prime Factorization
If the numbers are larger, divide them into their prime factors. Multiplying the common prime factors raised to the smaller exponent yields the greatest common factor (GCF). Multiplying each prime factor to the higher exponent yields the least common multiple (LCM). For instance, 20 and 28:
20 = 2² × 5
28 = 2² × 7
GCF = 2² = 4
LCM = 2² × 5 × 7 = 140
A Quick Way to Check Your Answer
In the case of two positive integers, GCF x LCM = First integer x Second integer.
Let us consider the following example: 18 = 2 x 3² and 30 = 2 x 3 x 5. We get GCF to be 6 and LCM to be 90. So 6 x 90 = 540 and 18 x 30 = 540. Both the answers are correct.
On the TI-34 MultiView: gcd( ) and lcm( )
Both features can be found under the MATH feature on the TI-34 MultiView. According to Texas Instruments, they are listed as lcm(n1, n2) and gcd(n1, n2). “gcd” stands for greatest common divisor and is synonymous with GCF.
Press MATH to access the math menu.
Select either lcm or gcd.
Type in the first number, followed by the separator key and then the second number.
Press ENTER.
Examples include lcm(4, 6) = 12 and gcd(4, 6) = 2.
Two Easy Mistakes
Mistaking factors and multiples. Factors are those which can divide a number without leaving any remainder. Multiples are the result of multiplying a number by other whole numbers.
Finding only common factors. 2 is a common factor of 24 and 36, but that doesn’t mean it’s the highest one. Look for a higher common factor.
FAQs
What is the difference between GCF and LCM?
GCF is the greatest common factor of the two numbers. The LCM is the least common multiple of the two numbers.
Can GCF and LCM be equal?
Sure, but that would be true only if the two numbers are equal. In case of 7 and 7, both the GCF and the LCM are 7.
Why does GCF help with fractions?
You reduce the fraction in one step when you divide the numerator and denominator by their GCF.
Why does LCM help with fractions?
When adding and subtracting fractions with different denominators, you must utilize LCM to determine the LCD.
What happens when one of the numbers is a multiple of the other?
The GCF will be the smaller figure, and the LCM will be the larger figure. The LCM is 20 and the GCF of 5 and 20 is 5.
Can the GCF or LCM of three integers be found?
Indeed. When prime factorization is used, only the primes shared by all three numbers are included in the GCF, and each prime's highest power is included in the LCM. For 4, 6, and 8, the LCM would be 24 and the GCF would be 2.
Is it possible that GCF is greater than any of those numbers?
No, because the GCF cannot be greater than the smallest number and LCM cannot be less than the greatest number.
On a TI-34 MultiView calculator, what does gcd mean?
gcd stands for greatest common divisor, which is the same as GCF.
Is it possible to determine them without using a calculator?
Yes, by listing factors or multiples or through prime factorization. A calculator is always helpful to verify the answer.
TI34Calc is an independent educational site and is not affiliated with Texas Instruments. Key names are given for the TI-34 MultiView for reference; check your calculator’s manual for your exact model.