how to find lcm and hcf
Answers
⏩ Answer :
▶ Highest Common Factor (HCF)
The largest number that divides two or more given numbers is called the Highest common factor (HCF) of those numbers.
Methods to find HCF
↪ Division method
This method is applicable for finding the HCF of two numbers. This method uses successive division to find the HCF. To find the HCF of two numbers N1 and N2, the smaller of the two, say N1, divides N2. The remainder R1 then divides N1 followed by the remainder R2 dividing R1, and so on till a remainder of 0 is reached.
↪ Prime factorisation Method
Writing a number as a product of its prime factors is called prime factorization. For example,
240=24×3×5 After prime factorization of the numbers, common factors are checked for. The HCF is the product of all such common prime factors, with their index being the least of those present in the prime factorised form.For example,
The HCF of 96, 144 and 240 can be found by prime factorization of these numbers. 96=25×31
144=24×32
240=24×31×51
HCF=24×31=48
▶ Least Common Multiple (LCM)
It is the lowest number which is divisible by all given numbers
Methods to find LCM
↪ Division method
Successive simultaneous division of numbers by prime factors.
↪ Prime factorisation Method
After performing prime factorisation of numbers, all prime numbers in their highest index are selected and multiplied to get the LCM. For example,
The LCM of 96, 144 and 240 can be found by prime factorization of these numbers.
96=25×31
144=24×32
240=24×31×51
LCM=25×32×51=1440
✔ Hope it may helps u...!!! ☺
Methods for finding LCM
( i ) By Factorization method
According to this method, firstly we have to write down the prime factors of the given number. Then, the LCM is the product of the highest powers of all the factors.
( ii ) By Prime Factors Method
According to this method, firstly we have to resolve the given numbers into their prime factors and then find the product of the highest power of all the factors that occur in the given numbers.
Methods for finding HCF
( i ) By Division Method
According to this methods, we have to divide the largest number by the smaller number. After dividing the largest number by the smaller number we get the remainder and divide the divisor by remainder. We have to repeat this process until no remainder left. In this process the last divisor in the desired greatest common divisor.
( ii ) By prime Factorization method
According to this method, we have to write the given number into prime factors and then find the product of all prime factors common to all the numbers. This product is the required HCF.