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Find the LCM (Least Common Multiple) of these groups of numbers. The first one has been set out for you.

a. 15 and 20

- Multiples of 15: 15, 30, ...
- Multiples of 20: 20, 40, ...
- The LCM of 15 and 20: ...

b. 3, 5, and 9

c. 4, 8, and 12

Answer :

To find the least common multiple (LCM) of two or more numbers, we need to identify the smallest number that is a multiple of each of the numbers. Let's look at each part of the question step by step:

a. LCM of 15 and 20

1. Write out some multiples of each number:
- Multiples of 15: 15, 30, 45, 60, 75, ...
- Multiples of 20: 20, 40, 60, 80, ...

2. Identify the smallest common multiple:
- Looking at the lists, the first common multiple is 60.

Therefore, the LCM of 15 and 20 is 60.

b. LCM of 3, 5, and 9

1. Write out some multiples of each number:
- Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, ...
- Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, ...
- Multiples of 9: 9, 18, 27, 36, 45, ...

2. Identify the smallest common multiple:
- The first common multiple among these numbers is 45.

Therefore, the LCM of 3, 5, and 9 is 45.

c. LCM of 4, 8, and 12

1. Write out some multiples of each number:
- Multiples of 4: 4, 8, 12, 16, 20, 24, 28, ...
- Multiples of 8: 8, 16, 24, 32, ...
- Multiples of 12: 12, 24, 36, ...

2. Identify the smallest common multiple:
- The first common multiple among these numbers is 24.

Therefore, the LCM of 4, 8, and 12 is 24.

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