Questions: What is the least common multiple of 7 and 16?

What is the least common multiple of 7 and 16?
Transcript text: What is the least common multiple of 7 and $16 ?$
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Solution

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Solution Steps

Step 1: Identify the numbers

The numbers given are 7 and 16.

Step 2: Find the prime factors
  • The prime factors of 7 are \(7\) (since 7 is a prime number).
  • The prime factors of 16 are \(2^4\) (since \(16 = 2 \times 2 \times 2 \times 2\)).
Step 3: Calculate the least common multiple (LCM)

The LCM is found by taking the highest power of each prime factor present in the numbers:

  • The highest power of 2 is \(2^4\).
  • The highest power of 7 is \(7\).

Thus, the LCM is \(2^4 \times 7 = 16 \times 7 = 112\).

Final Answer

\(\boxed{112}\)

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