Question
Find the $LCM$ of $40, 48$ and $45.$
✓
Answer
The prime factorizations of $40, 48$ and $45$ are given as follows:
$40 = 2 \times 2 \times 2 \times 5$
$48 = 2 \times 2 \times 2 \times 2 \times 3$
$45 = 3 × 3 × 5$
The prime factor $2$ appears maximum number of times which is four, in the prime factorisation of $48$, the prime factor $3$ occurs maximum number of two times in the prime factorisation of $45$, The prime factor $5$ appears one time in the prime factorisations of 40 and $45,$ we take it only once.
Therefore, we have required $LCM = (2 \times 2 \times 2 \times 2) \times (3 \times 3) \times 5 = 720$
$40 = 2 \times 2 \times 2 \times 5$
$48 = 2 \times 2 \times 2 \times 2 \times 3$
$45 = 3 × 3 × 5$
The prime factor $2$ appears maximum number of times which is four, in the prime factorisation of $48$, the prime factor $3$ occurs maximum number of two times in the prime factorisation of $45$, The prime factor $5$ appears one time in the prime factorisations of 40 and $45,$ we take it only once.
Therefore, we have required $LCM = (2 \times 2 \times 2 \times 2) \times (3 \times 3) \times 5 = 720$
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