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Chapter 5: Problem 68

Find the least common multiple of the numbers. 150 and 480

Short Answer

Expert verified
The least common multiple of 150 and 480 is 2400.

Step by step solution

01

Prime Factorization

Find the prime factors of both numbers. For 150, the prime factorization is \(2^1 * 3^1 * 5^2\). For 480, the prime factorization is \(2^5 * 3^1 * 5^1\).
02

Find the Highest Power of Each Prime Factor

For each prime factor, select the highest power that occurs in the factorizations of either number. This gives us: \(2^5, 3^1, 5^2\).
03

Calculate the LCM

Multiply these values together to find the LCM. So, the LCM of 150 and 480 is \(2^5 * 3^1 * 5^2 = 2400\).

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Most popular questions from this chapter

Determine whether each statement makes sense or does not make sense, and explain your reasoning. There's no end to the number of geometric sequences that I can generate whose first term is 5 if I pick nonzero numbers \(r\) and multiply 5 by each value of \(r\) repeatedly.

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=20, r=-4\)

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. \(0.0004,-0.004,0.04,-0.4, \ldots\)

What is a sequence? Give an example with your description.

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{40}\), when \(a_{1}=6, r=-1\).
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