Question

How do you find the least common multiple of \[18{m^2},24nm\] ?

Answer 1

Hint: We know that the least common multiple is also known as LCM. We will use a prime factorization method to find the LCM of the given problem. We will write each of the given numbers as the product of its prime factors and the LCM is a number which is a multiple of two or more than two numbers.

Complete step-by-step answer:
We have to find the LCM of \[18{m^2}\] and \[24nm\] .
Let’s write the prime factors of \[18{m^2}\]
 \[18{m^2} = 2 \times 3 \times 3 \times m \times m\] .
Let’s write the prime factors of \[24nm\]
 \[24nm = 2 \times 2 \times 2 \times 3 \times n \times m\]
We know that the LCM contains the factors of each number but without any duplicates.
 \[ \Rightarrow LCM{\text{ }}of{\text{ }}18{m^2}{\text{ }}and{\text{ }}24nm = 2 \times 3 \times m \times 2 \times 2 \times 3 \times n \times m\]
 \[ \Rightarrow LCM{\text{ }}of{\text{ }}18{m^2}{\text{ }}and{\text{ }}24nm = 72{m^2}n\]
Hence, the least common multiple of \[18{m^2},24nm\] is \[72{m^2}n\] .
(In case of variables we just write as it is and we find the LCM of them.)
So, the correct answer is “\[72{m^2}n\]”.

Note: We also have HCF or the highest common factor. If they asked us to find the HCF of \[18{m^2},24nm\] .
Since the greatest number which divides each of the two or numbers is called HCF or highest common factor. Also from using above prime factors we can say that the HCF of \[18{m^2},24nm\] is \[2 \times 3 \times m = 6m\] .