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Find the LCM of 18,72.

Find the LCM of $18$ , $72$ .

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Cube roots of positive perfect cubes

Full solution

Q. Find the LCM of

18

,

72

.

List Prime Factors: List the prime factors of each number. $\newline$ $18 = 2 \times 3 \times 3 = 2 \times 3^2$ $\newline$ $72 = 2 \times 2 \times 2 \times 3 \times 3 = 2^3 \times 3^2$
Identify Highest Powers: Identify the highest powers of all prime factors present in the numbers. $\newline$ For $2$ : The highest power is $2^3$ (from $72$ ). $\newline$ For $3$ : The highest power is $3^2$ (from both $18$ and $72$ ).
Multiply Highest Powers: Multiply these highest powers to find the LCM. $\newline$ LCM = $2^3 \times 3^2$ $\newline$ LCM = $8 \times 9$ $\newline$ LCM = $72$

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