Resolved: "How do you find the Least common multiple..."

Kade Frost

Answered question

2022-02-04

How do you find the Least common multiple of

18 m^{2}, 24 n m

venenolundicoofw

Beginner2022-02-05Added 12 answers

The lcm is the product of all the factors raised to the highest power they have in the given terms.
We can rewrite

18 m^{2} as 2 \cdot 3^{2} \cdot m^{2}

, and we can rewrite

24 n m as 2^{3} \cdot 3 \cdot n \cdot m

.
The highest power of 2 appears in the 2nd term:

2^{3}

.
The highest power of 3 appears in the 1st term:

3^{2}

.
The highest power of m appears in the 1st term:

m^{2}

.
The highest power of n appears in the 2nd term: n.
The

lcm (18 m^{2}, 24 n m)

is just the product of all of these pieces:

lcm (18 m^{2}, 24 n m) = 2^{3} \cdot 3^{2} \cdot m^{2} \cdot n = 72 m^{2} n

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