Why is 24 the LCM of 6 and 8?

Answer 1

LCM stands for least common multiple, not all the common multiples just the smallest one.

One of the methods to find LCM is to write down the multiples of both numbers:

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54,...

Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72,...

As we can see clearly 24 and 48 are common multiples in the first 9 multiples of 6 and 8 but 24 is the smallest multiple so it is the LCM.

Another explanation:

If we multiply 6 and 8 we get a common multiple.

6 x 8 = 48. 48 can be written as 2 x 2 x 2 x 2 x 3.

And we can say: common multiple of 6 and 8 = 2 x 2 x 2 x 2 x 3.

A number is common multiple of 6 and 8 only if it has 2 x 3(6) and 2 x 2 x 2(8).

In case of 48 we have four 2s but we require only three because 8 is expressed with maximum number of 2s.

So, 48 = 2 x 2 x 2 x 2 x 3 = 2 x 2 x 2 x 3 x 2.

So we can remove one 2 and we get:

Common multiple of 6 and 8 = 2 x 2 x 2 x 3 = 24.

Now we can't remove any 2 so, 24 is the LCM.

Answer 2

Because 24 is the smallest positive integer that both 6 and 8 divide into evenly with no remainder.

Answer 3

Because 6 can go into 24 four times whiles 8 can also go into 24 three times.