LCM of 5 and 9

Understand the Problem

The question is asking for the least common multiple (LCM) of the numbers 5 and 9, which involves finding the smallest number that is a multiple of both 5 and 9.

45

The least common multiple of 5 and 9 is 45.

Steps to Solve

1. Prime Factorization of 5

5 is a prime number, so its prime factorization is simply 5.

1. Prime Factorization of 9

9 is not a prime number. Its prime factorization is: $$9 = 3^2$$

1. Determine the Highest Powers of Prime Factors

The LCM is found by determining the highest power of each prime factor that appears in the factorizations of both numbers. From the prime factorizations, we have:

• For 5: $$5^1$$

• For 9: $$3^2$$

1. Multiply the Highest Powers of Each Prime Factor

The LCM is obtained by multiplying these highest powers together:

$$LCM(5, 9) = 5^1 * 3^2 = 5 * 9 = 45$$

Therefore, the LCM of 5 and 9 is 45.

The least common multiple of 5 and 9 is 45.

The concept of the LCM is useful in various areas of mathematics and everyday life, such as calculating time intervals and aligning schedules.

Tips

A common mistake is to add the prime factors instead of multiplying their highest powers. Always remember to use multiplication when calculating the LCM.

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LCM of 5 and 9

Understand the Problem

The question is asking for the least common multiple (LCM) of the numbers 5 and 9, which involves finding the smallest number that is a multiple of both 5 and 9.

45

The least common multiple of 5 and 9 is 45.

Steps to Solve

1. Prime Factorization of 5

5 is a prime number, so its prime factorization is simply 5.

1. Prime Factorization of 9

9 is not a prime number. Its prime factorization is: $$9 = 3^2$$

1. Determine the Highest Powers of Prime Factors

The LCM is found by determining the highest power of each prime factor that appears in the factorizations of both numbers. From the prime factorizations, we have:

• For 5: $$5^1$$

• For 9: $$3^2$$

1. Multiply the Highest Powers of Each Prime Factor

The LCM is obtained by multiplying these highest powers together:

$$LCM(5, 9) = 5^1 * 3^2 = 5 * 9 = 45$$

Therefore, the LCM of 5 and 9 is 45.

The least common multiple of 5 and 9 is 45.

The concept of the LCM is useful in various areas of mathematics and everyday life, such as calculating time intervals and aligning schedules.

Tips

A common mistake is to add the prime factors instead of multiplying their highest powers. Always remember to use multiplication when calculating the LCM.

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The text passage provides a detailed explanation of how to find the least common multiple (LCM) of 5 and 9, including the problem statement, solution, and steps to solve it.

TYPE: SINGLE_QUESTION_WITH_ANSWER