Prime factors, lowest common multiple and highest common factor can help us to solve real world problems. This is a useful area of mathematics that will aid your understanding of number.
The lowest/least common multiple (abbreviated to LCM) is the lowest number that is a multiple of two or more subject-numbers.
For example, the common multiples of 4 and 5 are 20, 40, 60, 80 and so on.
These are the numbers that are multiples of both 4 and 5.
The LCM is therefore 20, as this is the lowest of all the common multiples.
Example one
Find the LCM of 6 and 10.
If we write out the 6 times table, we get: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72.
If we write out the 10 times table, we get: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120.
So the LCM of 6 and 10 is 30.
Example two
Find the LCM of 12 and 36.
If we write out the 12 times table, we get: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144...
If we write out the 36 times table, we get: 36, 72, 108, 144, 180, 216...
From the times tables above, we can see that all the numbers in the 36 times table appear in the 12 times table.
The LCM of 12 and 36 is 36.
Sometimes we may be asked to find the LCM of more than two numbers. The process is exactly the same, although this does increase the difficulty slightly.
Example three
Find the LCM of 3, 4 and 5.
If we write out the 3 times table, we get: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60.
If we write out the 4 times table, we get: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80.
If we write out the 5 times table, we get: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100.
Note that in order to find a common multiple, we had to write out far more than 12 numbers in each times table.
