Multiples are products of natural numbers.

Look at the multiplications of 3 below:

1 x 3 = 3

2 x 3 = 6

3 x 3 = 9

4 x 3 = 12

5 x 3 = 15

6 x 3 = 18

7 x 3 = 21

8 x 3 = 24

Hence, the multiples of**3 are 3, 6, 9, 12, 15, 18, 21, 24**

1 x 3 = 3

2 x 3 = 6

3 x 3 = 9

4 x 3 = 12

5 x 3 = 15

6 x 3 = 18

7 x 3 = 21

8 x 3 = 24

Hence, the multiples of

Look at the multiplications of 4 below:

1 x 4 = 4

2 x 4 = 8

3 x 4 = 12

4 x 4 = 16

5 x 4 = 20

6 x 4 = 24

Hence, the multiples of**4 are 4, 8, 12, 16, 20, 24**

1 x 4 = 4

2 x 4 = 8

3 x 4 = 12

4 x 4 = 16

5 x 4 = 20

6 x 4 = 24

Hence, the multiples of

The common multiples of 3 and 4 shown above are 12 and 24. Therefore the **least common multiple of 3 and 4 is 12**.

For the GCD, the divisor (factor) has to be common to use it. For the LCM, if the smallest factor does not divide a number in the table, the number is retained. For example, we can find the LCM of 8, 12, 18, and 20 using tables as shown in the table below:

To get the LCM, we multiply the prime factors;

In the first row, 8 ÷ 2 = 4, 12 ÷ 2 = 6, 18 ÷ 2 = 9, and 20 ÷ 2 = 10,

In the second row, 4 ÷ 2 = 2, 6 ÷ 2 = 3, and 10 ÷ 2 = 5. However, 9 is not divisible by 2, therefore we retain it as it is; 9.

When using tables, always use the least prime factor, in the example below, its 2. As demonstrated above, the factor 2 is followed by 3 and then 5.

1. What is the LCM of 48, 100, and 72.

*Method 1: Using Prime Factorization:*

48: 2 x 2 x 2 x 2 x 3 = 2^{4} x 3^{1}

100: 2 x 2 x 5 x 5 = 2^{2} x 5^{2}

72: 2 x 2 x 2 x 3 x 3 = 2^{3} x 3^{2}

Now, to find the LCM, you take the highest power of each prime factor: The highest power of 2 that appears is 2^{4}.

The highest power of 3 that appears is 3^{2}.

The highest power of 5 that appears is 5^{2}.

Multiply these highest powers together to find the LCM:

LCM =^{4} x 3^{2} x 5^{2}

LCM = 16 x 9 x 25

LCM = 3600

So, the LCM of 48, 100, and 72 is 3600.

48: 2 x 2 x 2 x 2 x 3 = 2

100: 2 x 2 x 5 x 5 = 2

72: 2 x 2 x 2 x 3 x 3 = 2

Now, to find the LCM, you take the highest power of each prime factor: The highest power of 2 that appears is 2

The highest power of 3 that appears is 3

The highest power of 5 that appears is 5

Multiply these highest powers together to find the LCM:

LCM =

LCM = 16 x 9 x 25

LCM = 3600

So, the LCM of 48, 100, and 72 is 3600.

To get the LCM, we multiply the prime factors;

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