Least Common Multiple
Date: 3/29/96 at 11:8:1 From: JONATHAN FIELDS Subject: least common multiples Hi Dr. Math. The question I have is about how to find the least common multiples from a set of numbers. I know that a multiple of a number has that number as one of its factors. What is the least common multiple for the numbers 5 and 25? Is there a stated rule or definition for least common multiples? Thanks!
Date: 3/30/96 at 16:57:26 From: Doctor Sebastien Subject: Re: least common multiples Hi, The least common multiple (L.C.M.) of a set of numbers is the smallest number that is a multiple of all numbers in the set. The way I was told to find the LCM of a set of numbers was 1. align them in a line. 2. Then divide all numbers by an appropriate integer. 3. If any number is not divisible by that integer, don't divide that number and leave it untouched. 4. Repeat steps 2 and 3 until all 1's are obtained. 5. Then multiply all the divisors together. The answer is the LCM. To better explain what I mean, I will find the LCM of 5 and 25. STEP 1: 5, 25 1, 5 ------- STEP 2: 5 | 5, 25 1, 1 -------- STEP 2: 5 | 1, 5 In the previous step, the 1 is left untouched because it is not divisible by 5. The LCM is then 5*5 = 25. I hope I have been helpful. -Doctor Sebastien, The Math Forum
Date: 3/30/96 at 17:7:18 From: Doctor Ken Subject: Re: Dr. Math -- least common multiples Hello! Here's another way to think about doing Least Common Multiples: Since the least common multiple of two numbers is the smallest number that is a multiple of both the other numbers, you could also think of that as being the smallest number that contains all the _factors_ of the first two numbers. So let's say we want to find the LCM of 28 and 42: Well, let's list all the prime factors: 28 = 2*2*7 42 = 2*3*7 So our LCM is going to have to be divisible by 4 (which is 2*2), 3, and 7. Do you see why? So the LCM of 28 and 42 is 4*3*7 = 84. Note that if we write our numbers as 28 = 2*2*7 = 2^2 * 3^0 * 7^1 42 = 2*3*7 = 2^1 * 3^1 * 7^1, Then we can just take the biggest exponents and call that our number: LCM = 2^2 * 3^1 * 7^1 = 84. Hope that helps! -Doctor Ken, The Math Forum
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