H.C.F. & L.C.M. Interview Questions & Answers

H.C.F. & L.C.M.

40 Questions

Practice Problems

40 Questions

Common factor = a number which divides two or more given numbers exactly
H.C.F. (Highest Common Factor) = greatest number that divides each of two or more numbers exactly (also called G.C.D. or G.C.M.)
Common multiple = a number exactly divisible by each of two or more given numbers
L.C.M. (Least Common Multiple) = smallest number exactly divisible by each of two or more given numbers
Product of two numbers = L.C.M. of the numbers × H.C.F. of the numbers
For two numbers x and y: x × y = L.C.M.(x, y) × H.C.F.(x, y)
Before finding H.C.F. or L.C.M., all quantities must be expressed in the same unit

Prime Factor Method: express each number as product of prime factors → H.C.F. = product of common factors (with lowest powers)
Division Method (two numbers): divide greater by smaller; divide previous divisor by remainder; repeat until remainder = 0; H.C.F. = last divisor
Division Method (more than two numbers): find H.C.F. of any two numbers; find H.C.F. of that result with next number; repeat until all numbers used; H.C.F. of last step = required H.C.F.

Prime Factor Method: resolve each number into prime factors → L.C.M. = product of all factors taken with highest powers occurring
Division Method: write numbers in a line; divide by a prime number that divides at least two numbers exactly; bring down undivided numbers; repeat until remaining numbers are co-prime; L.C.M. = product of all divisors and last line of numbers

Step 1: Make equal number of decimal places in all numbers by suffixing zeros
Step 2: Find H.C.F./L.C.M. of the numbers ignoring the decimal point
Step 3: Place decimal point in the result, leaving as many digits on the right as in each original number

L.C.M. of fractions = L.C.M. of numerators / H.C.F. of denominators
H.C.F. of fractions = H.C.F. of numerators / L.C.M. of denominators
Treat whole numbers as fractions with denominator 1 when mixed with fractions
H.C.F. of a set of fractions is always a fraction; L.C.M. may be a fraction or an integer