least common multiple of 9 and 5
Understand the Problem
The question is asking to find the least common multiple (LCM) of the numbers 9 and 5. The LCM is the smallest number that is a multiple of both given numbers.
Answer
45
Answer for screen readers
The final answer is 45
Steps to Solve
- Prime factorization of both numbers
Identify the prime factors of both numbers.
For 9: $ 9 = 3^2 $ For 5: $ 5 = 5^1 $
- Identify the highest powers of all prime factors
The prime factors are 3 and 5. The highest powers of these prime factors are:
$$ 3^2 ext{ and } 5^1 $$
- Multiply the highest powers of all prime factors
Multiply the highest powers of each prime number to get the LCM:
$$ LCM(9, 5) = 3^2 \times 5^1 $$
$$ 3^2 = 9 $$ $$ 5^1 = 5 $$
Therefore,
$$ LCM(9, 5) = 9 \times 5 = 45 $$
The final answer is 45
More Information
The least common multiple (LCM) is useful for finding the smallest shared interval for repeating events or cycles.
Tips
A common mistake is to confuse the greatest common divisor (GCD) with the least common multiple (LCM). Remember that LCM is larger than or equal to both numbers.
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