Question

How do you find LCM and GCF (of two or more numbers) using prime factorization (prime factor trees?)?

Answer 1

Hint: LCM: Least Common Multiple : Least common multiple can be found by multiplying the highest exponent prime factors of the given numbers . For this we have to calculate the prime factor of the numbers . GCF: Greatest Common factor: It’s the greatest number which is a factor of both of them. In simple words it can be described as the largest positive number that divides evenly both the numbers and thus gives a zero remainder.

Complete step by step solution:
Let us consider two numbers ,
$14$ and $7$
Now we know we have to do prime factorization of all the numbers $14$ and $7$ .
Prime factorization: It’s the process where the original given number is expressed as the product of
prime numbers.
So prime factorization of $14$ :
$14 = 2 \times 7$
Prime factorization of $7$:
$7 = 7$
Least common multiple can be found by multiplying the highest exponent prime factors of $14$ and $7$.
Therefore, we can write ,
LCM of $14$ and $7$ is given as ,
$ = 2 \times 7$
$ = 14$
Therefore, we can write that the LCM of $14$ and $7$ is $14$ .
Now in order to get the GCF we have to multiply the common terms with each other.
Therefore, we can write ,
GCF of $14$ and $7$ is given as ,
$ = 7$
Therefore, we can write that the GCF of $14$ and $7$ is $7$ .

Note: Questions similar in nature as that of above can be approached in a similar manner and we can solve it easily. The above question can also be done by simply listing all the possible factors of both the given numbers and then taking the greatest common factor by just comparing the list of factors.