Finding common multiples is a basic arithmetic skill taught in primary school mathematics. To find the common multiples of two numbers like 12 and 18, we first need to list out their individual multiplication tables.
A quick trick: Once you find the LCM (which is 36), every common multiple will simply be a multiple of 36 (36x1=36, 36x2=72, 36x3=108).
Numbers have an infinite number of multiples, but they only have a limited number of factors.
A multiple is the result of multiplying a number by an integer (1, 2, 3, etc.). Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144...
Multiples of 18: 18, 36, 54, 72, 90, 108, 126, 144, 162...
Now, we look at both lists and find the numbers that appear in both of them. The common multiples of 12 and 18 are: 36, 72, 108, 144... and so on. (This pattern will continue infinitely).
The Lowest Common Multiple (LCM) is simply the smallest number that appears in both lists. From our list, the LCM of 12 and 18 is 36.
The factors of 12 are (1,2,3,4,6,12) and 18 are (1,2,3,6,9,18). The highest number common to both lists is 6. So, the HCF is 6.
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