Q.18 - Intermediate Algebra

Question

In the following exercises, find the least common multiple of each pair of numbers using the prime factors method.

60, 72

Step-by-Step Solution

Answer

The least common multiple of 60 and 72 is 360.

Step 1. Given information

The given numbers are 60 and 72.

The least common multiple of the given numbers is to be determined using prime factors.

Step 2. Calculating the prime factors

For prime factorization, the given number is to be factored such that all the factors are prime numbers.

$$\begin{gathered} 60=2·30 \\ 60=2·2·15 \\ 60=2·2·3·5 \end{gathered}$$

The factors are all primes here and cannot be further factored.

$$\begin{gathered} 72=2·36 \\ 72=2·2·18 \\ 72=2·2·2·9 \\ 72=2·2·2·3·3 \end{gathered}$$

The factors are all primes here and cannot be further factored.

Step 3. Calculating least common multiple

To determine LCM, the prime factors of both the numbers are to be considered and the factors that are present in both are to be taken whereas the repeated factors are to be taken only once.

$$\begin{gathered} \mathrm{LCM}=2·2·2·3·3·5 \\ \mathrm{LCM}=360 \end{gathered}$$

Step 4. Conclusion

Therefore, the least common multiple of 60 and 72 is 360.