About LCM and HCF
LCM i.e least common multiple is a number which is multiple of two or more than two numbers. For example: The common multiples of 3 and 4 are 12,224 and so on.
Therefore, LCM is smallest positive number that is multiple of both. Here LCM is 12.. HCF i.e. Maths tricks Highest common factor are those integral values of number that can divide that number. LCM and HCF problems are very important part of all competitive exams.
Some important LCM and HCF tricks.
1. Product of two numbers = Their HCF. * Their LCM
2. HCF fo given numbers always divides their LCM.
3. HCF of given fractions = HCF of numerator/LCM of denominator
4. LCM of given fractions = LCM of numerator/ HCF of denominator
5. If d is the HCF of two positive integer a and b, then there exist d = am + bn
6. If p is prime and a,b are any integer then p / ab, This implies p /a or p / b
7. HCF of a given number always divides its LCM.
Most important points about LCM and HCF Problems.
1. Largest number which divides x,y,z to leave same remainder = HCF of Y-X, Z-Y, Z-X.
2. Largest number which divides x,y,z to leave remainder R (i.e. same) = HCF of X-R, Y-R, Z-R.
3. Largest number which divides x,y,z to leave same remainder a,b,c = HCF of X-A, Y-B, Z-C.
4. Least number which when divided by x,y,z and leaves a remainder R in each case = ( LCM of X,Y,Z) + R.
HCF and LCM Questions
LCM i.e least common multiple is a number which is multiple of two or more than two numbers. For example: The common multiples of 3 and 4 are 12,224 and so on.
Therefore, LCM is smallest positive number that is multiple of both. Here LCM is 12.. HCF i.e. Maths tricks Highest common factor are those integral values of number that can divide that number. LCM and HCF problems are very important part of all competitive exams.
Some important LCM and HCF tricks.
1. Product of two numbers = Their HCF. * Their LCM
2. HCF fo given numbers always divides their LCM.
3. HCF of given fractions = HCF of numerator/LCM of denominator
4. LCM of given fractions = LCM of numerator/ HCF of denominator
5. If d is the HCF of two positive integer a and b, then there exist d = am + bn
6. If p is prime and a,b are any integer then p / ab, This implies p /a or p / b
7. HCF of a given number always divides its LCM.
Most important points about LCM and HCF Problems.
1. Largest number which divides x,y,z to leave same remainder = HCF of Y-X, Z-Y, Z-X.
2. Largest number which divides x,y,z to leave remainder R (i.e. same) = HCF of X-R, Y-R, Z-R.
3. Largest number which divides x,y,z to leave same remainder a,b,c = HCF of X-A, Y-B, Z-C.
4. Least number which when divided by x,y,z and leaves a remainder R in each case = ( LCM of X,Y,Z) + R.
HCF and LCM Questions
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