Question

How are GCF and LCM alike?

Answer 1

Hint: From the question we are asked to say how GCF and LCM are alike. Actually, these two are not alike. But to find both we start by doing a prime factorization, but then you do something a little different. They both find things in common among a set of integers.

Complete step-by-step answer:
GCF is the greatest common factor and LCM is lowest common factor. These topics are related to factors of mathematics. We can calculate GCF and LCM of any two or more numbers. For the calculation of GCF of two number: at first we have to write factors of first given number and then write factors of second number. Then point out the common factors of those numbers and multiply them. The result obtained is GCF. Now, for LCM of two numbers: multiply two numbers and divide the result by GCF of same numbers. But for the prime number we may find LCM directly only by multiplication as they don't have common factors and GCF is $1$.
For example: Calculate GCF and LCM of \[16\] and \[24\].
For GCF,
Here the factors of \[16\] are \[2,~2,~2,2.~~\]
And the factors of \[24\]are \[2,~2,~2,~3.\]
Then, the common factors of \[16\] and \[24\] are \[2,~2\] and \[2\].
For GCF we will get,
\[\Rightarrow 2\times 2\times 2=8\]
So, GCF of \[16\] and \[24\] is \[8\].
For LCM,
\[\Rightarrow LCM=\dfrac{\left( multiplication\text{ }of\text{ }number \right)}{Their\text{ }GCF}\]
LCM of \[16\] and \[24\]
\[\Rightarrow \dfrac{\left( \text{ }16\times 24 \right)}{GCF}\]
\[\Rightarrow \dfrac{384}{8}\]
\[\Rightarrow 48\]
So, LCM of \[16\] and \[24\] is \[48\].

Note: Students should not confuse between the GCF and LCM. GCF and LCM are actually not alike at all and they are often easily confused. We tend to hear GREATEST and LOWEST when we hear these names. GREATEST makes us think BIG, while LOWEST makes us think small. The Greatest Common FACTOR of several numbers is the highest FACTOR (i.e., a small value) which divides INTO all of the given numbers. The largest possible value is the smallest of the given numbers. The Lowest Common MULTIPLE of several numbers is the first MULTIPLE (a big number) which is divisible BY all of the given numbers.