 # Quantitative Aptitude: Points to Remember for LCM and HCF

The experts of Jagranjosh.com have come forward to help the aspirants in attempting all the questions speedily with basic preparatory strategy. By providing basic concepts, we are trying to make the calculation faster than doing from long and traditional ones.

May 21, 2015 15:43 IST

The experts of Jagranjosh.com have come forward to help the aspirants in attempting all the questions speedily with basic preparatory strategy. By providing basic concepts, we are trying to make the calculation faster than doing from long and traditional ones.

• 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 an-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.