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HCF and LCM - II

Suvam Banerjee
17 Mar 0 0

Highest Common Factor (HCF): It is also called the Greatest Common divisor. When the greatest number divides perfectly two or more given numbers, the number is called HCF.

Least Common Multiple (LCM): The least number divisible by two or more given numbers; that least number is called LCM of the numbers.

Factor and Multiples: If a number m divides perfectly second number n, then m is called the factor of n and n is called multiple of m.

Rule 1 : 1st number * 2nd number = LCM*HCF

There are two methods for calculating HCF and LCM :

  • Factor Method
  • Division Method

If the ratio of two numbers is a:b, then numbers are ak and bk, where k is a constant and hence, HCF is k and LCM is abk.

Rule 2 : LCM of fractions = LCM of numerators / HCF of denominators

HCF of fractions = HCF of numerators / LCM of denominators

If there is no common factor between both numbers, then LCM will be the numbers' product.

When a number is divided by a,b or c, leaving remainders p,q or r respectively such that the difference between the divisor and reminder in each case is the same, i.e. (a-p)=(b-q)=(c-r) = t. The least number must be in the form of (k-t), where k is the LCM of a,b and c.

The largest numbers, which when divide a,b and c, give remainders p,q and r respectively, are given by HCF of (a-p), (b-q) and (c-r).

The largest number, which when dividing the numbers a,b and c the remainders are same then the largest number is given by HCF of (a-b), (b-c) and (c-a).

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