Question
Find the $LCM$ of $24$ and $90.$
✓
Answer
Clearly, The prime factorizations of $24$ and $90$ are:
$24 = 2 \times 2 \times 2 \times 3$
$90 = 2 \times 3 \times 3 \times 5$
In the above prime factorizations the maximum number of times the prime factor $2$ occurs is three for $24.$ Similarly, the maximum number of times the prime factor $3$ occurs is two for $90.$
The prime factor $5$ occurs only once in $90.$
Therefore, $LCM$ of $24$ and $90 = (2 \times 2 \times 2) \times (3 \times 3) \times 5 = 360$
$24 = 2 \times 2 \times 2 \times 3$
$90 = 2 \times 3 \times 3 \times 5$
In the above prime factorizations the maximum number of times the prime factor $2$ occurs is three for $24.$ Similarly, the maximum number of times the prime factor $3$ occurs is two for $90.$
The prime factor $5$ occurs only once in $90.$
Therefore, $LCM$ of $24$ and $90 = (2 \times 2 \times 2) \times (3 \times 3) \times 5 = 360$
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