Have problems in finding answers to your LCM and HCF Questions of different levels? Don't worry, we got the tool which can help you find answers to all your LCM and HCF Questions all in one place.
Here are some samples of LCM of Numbers calculations.
Here are some samples of HCF of Numbers calculations.
LCM and HCF Questions: If you are looking for a calculator to help you with LCM and HCF Questions then this is the right place for you. In this article, you can get Questions on HCF and LCM along with answers and explanations to help you get a hold of the concept more clearly. You can solve Least Common Multiple and Highest Common Factor questions over here of any level and of any type.
LCM and HCF are two entirely different terms in mathematics. The full form of LCM is Lowest Common Multiple or Least common multiple whereas HCF stands for Highest Common Factor.
The H.C.F interprets the greatest or highest factor present in between given two or more sets of numbers whereas L.C.M. defines the least or lowest number which is exactly divisible by two or more sets of numbers (exactly divisible means that they do not leave any remainder behind).
HCF of any given set of numbers can not be greater than any of them whereas LCM of a given set of numbers cannot be smaller than any of them.
H.C.F is also known as the greatest common factor (GCF) whereas LCM is also known as the Least Common Divisor.
There are several methods one can use to find the HCF and LCM of a given set of numbers.
HCF by Prime Factorization method
As we know that the factors of a number are exact divisors of that specific number.
To find the HCF of a given set of numbers by prime factorization,
LCM by Prime Factorization method
To calculate the LCM of any given number,
HCF by Division Method
To find the HCF by division method,
LCM by Division Method
To find the LCM by division method,
Evaluate HCF of 198 and 360 using the division method.
Firstly, on divide 60 by 198, the remainder is 162. Then, refer to 162 as the divisor and 198 as the dividend and conduct the division again. The remainder is 36. Take 36 as the divisor and 162 as the dividend and conduct the division again. Here the remainder is 18. Take 18 as the divisor and 36 as the dividend and conduct the division again. Finally, the remainder is 0.
The last divisor, 18, will be the HCF of 360 and 198.
Find the LCM of 30 and 60.
Let's evaluate the LCM of 30 and 60 using the prime factorization method.
Prime factorization of 30 = 2 × 3 × 5 and 60 = 2 × 2 × 3 × 5. Note these prime factors in their exponential form as, 30 = 2¹ × 3¹× 5¹ and 60 = 2² × 3¹× 5¹. Now, evaluate the product of only those factors that have the highest powers. Which will be, 2² × 3¹ × 5¹ = 4 × 3 × 5 = 60
Therefore, LCM(30,6) = 60
https://hcflcm.com/ has concepts like LCM and HCF to clear all your doubts and help learn and understand its concept along with their relevant calculators all under one roof.
To find HCF and LCM for fractions quickly the below formulas are used,
Least Common Multiple(LCM) = Least Common Multiple(LCM) of numerator/Highest Common Factor(HCF) of denominator
Highest Common Factor(HCF)= Highest Common Factor(HCF) of numerator/ Least Common Multiple(LCM)of denominator
The rule of HCF and LCM says that the product taken from two numbers is equal to the product of the LCM and HCF of those two numbers.
Let’s consider HCF and LCM of two numbers are 4 and 60 respectively, if one number is 12, then the second number can be found by, assuming it is X and using formulas,
Product of Numbers= Product of their HCF and LCM
12× X = 4×60
For two numbers 45 and 30, HCF is 15 because it is the largest number that can divide 45 and 30 completely. Similarly, LCM for 45 and 30 is 90, because it is the smallest number which can be divided by 45 and 30.