L.C.M and H.C.F based Questions – Important Formulas
Numerical Aptitude Notes for APSC Prelim CSAT Paper, SSC and Competitive Exams
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Factors and Multiples:
If number a divided another number b exactly, we say that a is a factor of b.
b is also a multiple of a.
Highest Common Factor (H.C.F.) or Greatest Common Divisor (G.C.D.)
The H.C.F. of two or more than two numbers is the greatest number that divides each of them exactly.
Two methods of finding the H.C.F. of a given set of numbers:
Factorization Method: Express the each one of the given numbers as the product of prime factors. The product of least powers of common prime factors gives H.C.F.
Division Method: To find the H.C.F. of two given numbers, divide the larger by the smaller one. Now, divide the divisor by the remainder. Repeat the process of dividing the preceding number by the remainder last obtained till zero is obtained as remainder. The last divisor is the H.C.F.
Least Common Multiple (L.C.M.)
The least number which is exactly divisible by each one of the given numbers is called their L.C.M.
There are two methods of finding the L.C.M. of a given set of numbers:
Factorization Method Resolve each one of the given numbers into a product of prime factors. Then, L.C.M. is the product of highest powers of all the factors.
Division Method: Arrange the given numbers in a rwo in any order. Divide by a number which divided exactly at least two of the given numbers and carry forward the numbers which are not divisible. Repeat the above process till no two of the numbers are divisible by the same number except 1. The product of the divisors and the undivided numbers is the required L.C.M. of the given numbers.
H.C.F. and L.C.M. of Fractions
H.C.F. = (H.C.F. of Numerators)/(L.C.M. of Denominators)
L.C.M. = (L.C.M. of Numerators)/(H.C.F. of Denominators)
Product of two numbers = Product of their H.C.F. and L.C.M.
Co-primes: Two numbers are said to be co-primes if their H.C.F. is 1.
Comparison of Fraction numbers
- Find the L.C.M. of the denominators of the given fractions.
- Convert each of the fractions into an equivalent fraction with L.C.M as the denominator, by multiplying both the numerator and denominator by the same number.
- The resultant fraction with the greatest numerator is the greatest.