What is the least common multiple of 4 8 10 and 20?

Answer 1

To get a start on this we need the prime factors of each number, and we add to the list as we move along through them.

The prime factors of 4 are 2 and 2.... so the result must have two 2s in it.

The prime factors of 8 are 2, 2 and 2... as the result already has two 2s, we need to add another. Now we know that the result must have three 2s in it.

The prime factors of 10 are 2 and 5.... there is already a 2 in the result so we must add one 5 to it. Now we know that the result must have three 2s and one 5.

The prime factors of 20 are 2, 2 and 5.... but we already have all those in the result.

Now we know that if we multiply three 2s and one 5 together the product will be the lowest number that will be a multiple of all our four given numbers.

2 x 2 x 2 x 5 = 40.

To prove that that is the Lowest Common Multiple, if we divide by each of our given numbers then the result of one of the divisions must be a Prime number.

40 / 4 = 10

40 / 8 = 5 .... as 5 is a prime number there is no lower number which 8 will divide evenly into and which will be a multiple of the other numbers.