HCF and LCM Formulas, Tips and Tricks to Solve Problems

Hello Aspirants, Under " HCF and LCM Formulas, Tips and Tricks to Solve Problems " we will discuss different formulas which govern the HCF and LCM as well as some shortcuts, tips and tricks to solve the problems based on HCF and LCM in any competitive exams.

• We can find HCF of two or more numbers by mainly two methods :

1. Prime Factorization Method
2. Long Division Method

Refer : Methods Used to Find HCF of two or more numbers for details.

• We can find LCM of two or more numbers by mainly two methods :

1. Prime Factorization method
2. Basic Line Division metod

Refer : Methods Used to Find LCM of two or more numbers for details.

• We can find HCF and LCM of a fraction by Formula :

1. HCF of a fraction = HCF of numerator / LCM of denominator
2. LCM of a fraction = LCM of numerator / HCF of denominator

Refer : HCF and LCM of Fractions and Decimals for details.

• Product of two numbers = Product of their H.C.F. and L.C.M.

This condition is only true for two given numbers. If H.C.F. and L.C.M. of three or more numbers are given, then this rule is not applicable.

• H.C.F. and L.C.M. of decimals 

1. Method A : To find H.C.F. or L.C.M. of 1.5, 2.6, 3.0 etc, consider these numbers without decimal point i.e 15, 26, 30 and solve using normal methods used to determine H.C.F. or L.C.M.. In the result, mark off as many decimal places as there are in each of the given number.
2. Method B : To find H.C.F. or L.C.M. of 2.5, 5.5, 7.5 etc, convert these numbers into fractions like 25/10, 55/10, 75/10 and used the formula used to find out HCF and LCM of fractions.

• Comparison of fractions

Step 1 : Find L.C.M. of denominators of given fractions.
Step 2 : Convert each fraction into equivalent fraction with L.C.M. as denominator, by multiplying both numerator and denominator by same number.
Step 3 : The resultant fraction with the greatest numerator is greatest.