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Tricks and Ways to solve the HCF and LCM problems

Some Tricks and Ways to solve the HCF and LCM problems

Find the HCF for given set of the numbers – You can use the above given method of finding out the factors or use the division method

Division Method- Divide the largest number with 2nd largest number and from remainder divide the 2nd largert number do this till remainder is zero.  Now the factor which brings in zero remainder is HCF for the largest and 2nd largest number. Use this HCF to divide the 3rd largest number and if the remainder is zero this also HCF of the 3 numbers if not, keep the process on till you get Zero and the factor will be HCF. 

Find the largest number of X digits  ( X =  3, 4 or 5) which is divisible by a, b, c or d.  The solutions to such problem is simple. Take largest digit of X digit say 4 then largest 4 digit no. is 9999, find out LCM of a, b, c, d and divide 9999 by this LCM, if there is a remainder ( R ) after division note it. Now subtract remainder  from  9999 so we get 9999- R.

Take this quiz to test your understanding of the concept.

Find least number which when divided by a, b, c, and d leaves  remainders  v, x, y, z . The solution to such problem is as follows. Find out (a-v), (x-b), (c-y), (d-z) in all probability these would be same say K.   Find out the LCM Of a, b, c, and d and subract the K from LCM this will be the answer

Represent A/ B in the most common form. Find out HCF of the A and B and divide the A and B to represent in lowest or simplest form

Finding out HCF of numbers with Decimal Places : Easy, make the numbers in common format with equal digits after decimal. Take the numbers as without decimals and find out HCF. Replace the decimal in HCF to get the correct answer

If the numbers are given in ratio a:b:c and HCF is given. Find out the number. Solution is very easy mutiply ratios with HCF to get the numbers

The sum of two numbers are given X and HCF is given, find out the number : Solution is to represent X = HCF (a+b)                        then X/HCF = a + b.  This can be represented as sum of the prime numbers. Once the prime number is identified it can be multiplied with HCF to find the original number

The LCM of two numbers is given and the ratios of the two numbers are given as a:b then find out the sum of the numbers: The solution is to represent  numbers ax and bx the LCM of the numbers is abx = given. Hence x can be derived and hence the sum of the numbers

Thats all I would suggest you should take a quiz to test out these concepts click here.

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December 18, 2010
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