How do you find the Least common multiple of 28, 14, 21?

Question

Telering3b · Accepted Answer

L.C.M(28,14,21)=84  Explanation:   There are two ways to find L.C.M(28, 14, 21)  First method:   List the multiples of 28, 14 and 21.   Choose the non-zero common multiple between the two lists.  Let us apply it:   Multiples of 28:  0, 28, 56, 84...  Multiples of 14 are:  0, 14, 28, 42, 56, 70, 84...  Multiples of 21 are:  0, 21, 42, 63, 84...  Therefore, L.C.M(28,14,21)=84  Second method:   Write the

Aaron Hughes · Accepted Answer

There are several ways to find the least common multiple (LCM) of three numbers.
Note that for any three positive integers a,b,c, we have:

L C M (a, b, c) = L C M (L C M (a, b), c)

That is, you can find the least common multiple of three numbers by finding the LCM of two of them then the LCM of the result and the third number.
In our example, first note that 28 is an exact multiple of 14 and hence:

L C M (28, 14) = 28

So:

L C M (28, 14, 21) = L C M (28, 21)

To find the LCM of 28 and 21 we can use another property of the LCM:

L C M (a, b) = \frac{a \cdot b}{G C F (a, b)}

where GCF(a,b) means the greatest common factor of a and b.
To find the GCF of 28 and 21 we can use this method:
- If the two numbers are equal, then that is the GCF.
- Otherwise replace the larger number by the result of subtracting the smaller number from the larger and repeat.
In our example, starting with 28, 21.

28 - 21 = 7

leaving us with 7, 21

21 - 7 = 14

leaving us with 7, 14

14 - 7 = 7

leaving us with 7, 7

G C F (28, 21) = 7

Answer:

L C M (28, 21) = \frac{28 \cdot 21}{7} = 28 \cdot 3 = 84

How do you find the Least common multiple of 28,

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