Quantitative Aptitude: Points to Remember for LCM and HCF

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• Product of two numbers = HCF of the numbers X LCM of the numbers
• The greatest number which divides the number x, y, and z, leaving remainder a, b and c, respectively = HCF of (x-a), (y-b), (z-c)

Note: This formula is true any number of numbers.

• The greatest number that will divide x, y, and z leaving the same remainder in each case is given by [ HCF of |x-y|, |y-z|, |z-x|…………]
• The least number which when divided by x, y, and z leaves the same remainder k in each case, is given by [LCM of (x,y,z)+k]

 Note: This formula is true any number of numbers.

• The least number which when divided by x, y, and z leaves the same remainder a,b, and c respectively is given by [LCM of (x,y,z)]-k

Where, k = (x-a), (y-b), (z-c)

• When the HCF of each pair of n number is a and their LCM is b, then the product of these number is given by a^n-1xb or (HCF)^n-1x LCM.’
• All the fractions must be in lowest terms. If they are not in their lowest term then conversion in lowest form is required before finding LCM and HCF.
• If two numbers are primes to each other (i.e.  coprimes) then their HCF is equal to 1, the numbers are prime to each other.