state the fundamental theorem of arithmetic and use it to find the lcm of 120 and 240

Dear Student,


FUNDAMENTAL THEOREM OF ARITHMETIC:

Every composite number can be expressed (factorised) as a product of primes, and this factorization is unique except for the order in which the prime factors occur.

While writing a positive integer as the product of primes, if we decide to write the prime factors in ascending order and we combine the same primes, then the integer is expressed as the product of powers of primes and the representation is unique.

So,we can say that every composite number can be expressed as the products of powers distinct primes in ascending or descending order in a unique way.

$$\begin{gathered} 120=\mathbf{2}\mathbf{\times }\mathbf{2}\mathbf{\times }\mathbf{2}\mathbf{\times }\mathbf{5}\mathbf{\times }\mathbf{3} \\ 240=2\times \mathbf{2}\mathbf{\times }\mathbf{2}\mathbf{\times }\mathbf{2}\mathbf{\times }\mathbf{5}\mathbf{\times }\mathbf{3} \\ LCM=2\times 2\times 2\times 2\times 5\times 3 \\ =240 \end{gathered}$$
​​​​
Regards!