Question

How do you find the LCM of \[96\] and \[108\]?

Answer 1

Hint: Prime factorization is a process of factoring a number in terms of prime numbers i.e., the factors will be prime numbers.
First, we are going to find the prime factorization of the given numbers.
From, there we can find the common multiplier.

Complete step-by-step solution:
As per the given question, we have to find the LCM of \[96\] and \[108\].
To find the LCM, at first, we will find the prime factorization of \[96\] and \[108\].
So, we can write \[96\] as,
\[96 = 2 \times 2 \times 2 \times 2 \times 2 \times 3\]
And, we can write \[108\] as,
\[108 = 2 \times 2 \times 3 \times 3 \times 3\]
So, LCM of \[96\] and \[108\] is \[2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3 = 864\]

Hence, the LCM of \[96\] and \[108\] is \[864\].

Note: In arithmetic and number theory , the least common multiple, lowest common multiple, or smallest common multiple of two integer a and b, usually denoted by lcm(a, b), is the smallest positive integer that is divisible by both a and b.
Since division of integers by zero is undefined, this definition has meaning only if a and b are both different from zero. However, some authors define lcm (a,0) as 0 for all a, which is the result of taking the lcm to be the least upper bound in the lattice of divisibility.
The lcm is the "lower common denominator" (lcm) that can be used before fractions can be added, subtracted or compared.
The lcm of more than two integers is also well-defined: it is the smallest positive integer that is divisible by each of them.
Prime factorization is defined as a way of finding the prime factors of a number, such that the original number is evenly divisible by these factors.
As we know, a composite number has more than two factors; therefore, this method is applicable only for composite numbers and not for prime numbers