LCM and HCF

LCM : Least Common Multiple 

The LCM of two or more numbers is the least number to be exactly divisible by each of them.

For example : LCM of 2,3,4 and 5 is 60.

HCF : Highest Common Factor 

The HCF of two or more numbers is the greatest number, which divides each of them exactly.

For example : HCF of 15, 18 and 30 is 3. 

TRICKS :

• Product of two numbers = HCF ✕ LCM of numbers
• The greatest number which divides the numbers x, y and z leaving remainders a, b and c respectively = HCF of (x-a),(y-b),(z-c)
• The greatest number that will divide x, y and z leaving the same remainder in each case            = [HCF of |x-y|, |y-z|, |z-x|]
• The least number, which when divided by x, y and z leaves the remainders a, b and c, respectively = [LCM of (x,y,z)] - m                                                                                                           where, m = (x-a) = (y-b) = (z-c)
• The least number , which when divided by x, y and z leaves the same remainder r in each case = [LCM of (x,y,z)] + r

TIPS :

• LCM of fractions = LCM of Numerators / HCF of Denominators
• HCF of fractions =  HCF of Numerators / LCM of Denominators