Finding the Least Common Multiple

To determine the least common multiple (LCM) of two or more numbers, begin by finding the prime factorization of each number. Then, highlight all the instances of each prime factor that is repeated most. Finally, multiply the highlighted factors to find the LCM. The LCM(54,60) will be found by following these four steps.

1

Find the Prime Factorization of the First Number

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Use a factor tree to determine the prime factorization of each number. For this situation, the factor tree of 54 will be drawn.

2

Find the Prime Factorization of the Second Number

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Follow the same process to find the prime factorization of the next number. Consider the factor tree of 60.

3

Match Prime Factors Vertically

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It can be helpful to write the prime factorizations of the numbers in a table. Place each prime factorization in a row of the table. Use columns for each factor and match common factors vertically when possible. The table for the prime factorization of 54 and 60 is shown here.

4

Bring Down the Primes in Each Column and Multiply

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Lastly, bring down the prime factors in each column of the table. This process is done with the table containing the prime factorizations of 54 and 60 below.

The product of these prime factors is the least common multiple of the numbers.

Prime Factors	Multiplication	LCM(54,60)
2, 2, 3, 3, 3 and 5	2*2*3*3*3*5	540

The least common multiple of 54 and 60, which can also be written as LCM(54,60), is 540.

It is worth noting that the least common denominator (LCD) of two or more fractions is the LCM of their denominators. Therefore, the LCM of their denominators must be found to find the LCD of two or more fractions.