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Chapter 5: Problem 63

Find the least common multiple of the numbers. 72 and 120

Short Answer

Expert verified
The least common multiple of 72 and 120 is \(2^{3} \times 3^{2} \times 5 = 360\).

Step by step solution

01

Prime Factorization

Find the prime factorization of both numbers. The prime factorization of 72 is \(2^{3} \times 3^{2}\) and the prime factorization of 120 is \(2^{3} \times 3 \times 5\).
02

Identify the Common Base

Identify common bases in the prime factorization of both numbers. Here, we have two common bases: 2 and 3.
03

Choose the Highest Power

Choose the highest power of each common base. The highest power of 2 in our factors is \(2^{3}\) and the highest power of 3 is \(3^{2}\). But from the factorization of 120, we also have an extra prime 5.
04

Multiply the Factors

Multiply together all the factors obtained in the previous step to find the LCM. So, the LCM of 72 and 120 is \(2^{3} \times 3^{2} \times 5\).

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Most popular questions from this chapter

Write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for \(a_{n}\) to find \(a_{7}\), the seventh term of the sequence. \(3,15,75,375, \ldots\)

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{40}\), when \(a_{1}=1000, r=-\frac{1}{2}\).

Use the appropriate formula shown above to find \(2+4+6+8+\cdots+200\), the sum of the first 100 positive even integers.

Write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for \(a_{n}\) to find \(a_{7}\), the seventh term of the sequence. \(0.0004,-0.004,0.04,-0.4, \ldots\)

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{20}\), when \(a_{1}=2, r=3\).
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