What is the LCM of 9 and 21?

Understand the Problem

The question is asking for the Least Common Multiple (LCM) of the numbers 9 and 21. To find the LCM, we need to identify the multiples of both numbers and determine the smallest multiple that they have in common.

Answer

$63$

Steps to Solve

Identify the multiples of each number

First, we will list the first few multiples of both 9 and 21.

For 9:

(9 \times 1 = 9)
(9 \times 2 = 18)
(9 \times 3 = 27)
(9 \times 4 = 36)
(9 \times 5 = 45)
(9 \times 6 = 54)
(9 \times 7 = 63)
(9 \times 8 = 72)
(9 \times 9 = 81)
(9 \times 10 = 90)

So, the multiples of 9 are: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90.

For 21:

(21 \times 1 = 21)
(21 \times 2 = 42)
(21 \times 3 = 63)
(21 \times 4 = 84)
(21 \times 5 = 105)
(21 \times 6 = 126)

So, the multiples of 21 are: 21, 42, 63, 84, 105, 126.

Find the common multiples

Next, we identify which multiples are common to both lists. From the lists we can see that the common multiple is 63.

Identify the smallest common multiple

Since we are looking for the Least Common Multiple (LCM), we take the smallest of the common multiples we found. Here, the smallest common multiple of 9 and 21 is 63.

The Least Common Multiple (LCM) of 9 and 21 is $63$.

More Information

The LCM is useful in various math problems, especially when adding, subtracting, or comparing fractions. In this case, it can help us find a common denominator.

Tips

A common mistake is to confuse LCM with GCD (Greatest Common Divisor). Remember, LCM is the smallest multiple shared by the numbers, while GCD is the largest divisor shared.

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