Question
Find the $LCM$ of $12$ and $18.$
✓
Answer
Clearly, we can see that common multiples of $12$ and $18$ are: $36, 72, 108$ etc
The lowest of these is $36.$
Now, Let us see another method to find $LCM$ of these two numbers.
The prime factorization of $12$ and $18$ are :
$12 = 2 \times 2 \times 3;$
$18 = 2 \times 3 \times 3$
In these prime factorizations, the maximum number of times the prime factor $2$ occurs is two; this happens for $12.$ Similarly, the maximum number of times the factor $3$ occurs is two; this happens for $18.$ The $LCM$ of the two numbers is the product of the prime factors counted the maximum number of times they occur in any of the numbers.
Thus, in this case: $LCM = 2 \times 2 \times 3 \times 3 = 36.$
The lowest of these is $36.$
Now, Let us see another method to find $LCM$ of these two numbers.
The prime factorization of $12$ and $18$ are :
$12 = 2 \times 2 \times 3;$
$18 = 2 \times 3 \times 3$
In these prime factorizations, the maximum number of times the prime factor $2$ occurs is two; this happens for $12.$ Similarly, the maximum number of times the factor $3$ occurs is two; this happens for $18.$ The $LCM$ of the two numbers is the product of the prime factors counted the maximum number of times they occur in any of the numbers.
Thus, in this case: $LCM = 2 \times 2 \times 3 \times 3 = 36.$
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