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Exercises Expressions, exponents and radicals

Example 2.52 from Prealgebra, 2.5 Prime Factorization and the Least Common Multiple

Prime Factorization and the Least Common Multiple: example 2.52

Find the LCM of $15$ and $20$ by listing multiples.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
List the first several multiples of $15$ and of $20 .$ Identify the first common multiple.

$\begin{array}{l} 15: 15, 30, 45, 60, 75, 90, 105, 120 \\ 20: 20, 40, 60, 80, 100, 120, 140, 160 \end{array}$

The smallest number to appear on both lists is $60,$ so $60$ is the least common multiple of $15$ and $20 .$

Notice that $120$ is on both lists, too. It is a common multiple, but it is not the least common multiple.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Find the least common multiple (LCM) of the given numbers: $9 and 12$

How did it go?

PreviousPrime Factorization and the Least Common Multiple: example 2.51 Next Prime Factorization and the Least Common Multiple: example 2.53

From Prealgebra (1st edition) by OpenStax (Rice University), section 2.5, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.