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60 and its multiples
5
Since the lowest common multiple of 3 and 5 is 15, the common multiples of 3 and 5 are the multiples of 15: 30, 45, 60, 75, 90, etc...
There are infinitely many common multiples of 3, 5 and 7, each one 105 larger than the previous one. Or to put it another way: the common multiples of 3, 5 and 7 are the multiples of their lowest common multiple which is 105. ie their common multiples are all the multiples of 105, of which there is no end - there is an infinite number of multiples of 105 (or any other number [except zero]).
5,3,4, and 2 have many common denominators. What is the least common denominator of all of them?Let's look at the multiples of each number. We do this because common denominators are really common multiples of the denominators. And the LCD is really just the least common multiple (LCM) of the denominators.Starting with 2, the 3, and 4 and last 5 we have the following lists of multiples:2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,68,603,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,604,8,12,16,20,24,28,32,36,40,44,48,52, 56,605,10,15,20,25,30,35,40,45,50,55,60So 60 is the first common multiple and it is the least common denominator of 2, 3, 4 and 5. Note that we could also factor 2, 3, 4 and 5 into primes (2, 3 and 5 already are) So we have 2, 3, 2^2 and 5 We take the largest exponent possible from each and we have 3 x 2^2 x 5 = 20 x 3 = 60. This is the faster way to do this.