Hello again! We are back with another topic. This time its LCM & HCF. Before we begin, let me remind you again that now we have our own server for mock test. If you are not yet register, register here, and try our mock tests.
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LCM or Least Common Multiple is the least number which can be exactly divisible by given number. Easiest way to find LCM is by factorization method. In this method we express each given in the product of prime factors. Product of highest powers of all the factors is LCM.
LCM of fraction = LCM of Numerators/ HCF of denominators.
Finding LCM when reminder is same = (LCM of numbers) + R.
Finding LCM, when reminder is different in each case :
Suppose you have to calculate the LCM of (x1,x2,x3) and reminder in each case is (r1, r2, r3).
Lets find common reminder R = (x1 - r1) = (x2 - r2) = (x3 - r3)
LCM = (LCM of x1, x2, x3) - R.
HCF or Highest Common Factor is the highest number that divides each of them exactly. Easiest method to find HCF is by factorization method. Express each number as product of prime factors. Product of least power of common prime factors will give you HCF.
HCF of fraction = HCF of Numerators/ LCM of denominators.
Finding HCF when reminder is same in each case = HCF [(n2 - n1)(n3-n2)(n3-n1)]
Find HCF when reminder is "R" = HCF[(n1 - R)(n2 - R)(n3 - R)]
Find HCF when reminder is different in each case = HCF[(n1 - r1)(n2 - r2)(n3 - r3)]
Product of two numbers = Product of their LCM & HCF
Another useful tip is : Ratio = value/HCF
Time for some exercise now.
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