find HCF and LCM
10,16 class 6th
Bilborailey
Answers
Answer:
The full forms of H.C.F. and L.C.M. are, Highest Common factor and Least Common Multiple, respectively. The H.C.F. defines the greatest factor present in between given two or more numbers, whereas L.C.M. defines the least number which is exactly divisible by two or more numbers. H.C.F. is also called the greatest common factor (GCF) and LCM is also called the Least Common Divisor.
To find H.C.F. and L.C.M. we have two important methods which are Prime factorisation method and division method. Both the methods we have learned in our earlier classes. The shortcut method to find both H.C.F. and L.C.M. is division method. Let us learn the relationship between HCF and LCM with the help of formula here. Also, we will solve some problems based on these two concepts to understand better.
HCF and LCM Definition
We know that the factors of a number are exact divisors of that particular number. Let’s proceed to the highest common factor (H.C.F.) and the least common multiple (L.C.M.).
HCF (Highest Common Factor)
As the rules of mathematics dictate, the greatest common divisor or the gcd of two or more positive integers happens to be the largest positive integer that divides the numbers without leaving a remainder. For example, take 8 and 12. The H.C.F. of 8 and 12 will be 4 because the highest number that can divide both 8 and 12 is 4.
LCM (Least Common Multiple)
In arithmetic, the least common multiple or LCM of two numbers say a and b, is denoted as LCM (a,b). And the LCM is the smallest or least positive integer that is divisible by both a and b. For example, let us take two positive integers 4 and 6.
Multiples of 4 are: 4,8,12,16,20,24…
Multiples of 6 are: 6,12,18,24….
The common multiples for 4 and 6 are 12,24,36,48…and so on. The least common multiple in that lot would be 12. Let us now try to find out the LCM of 24 and 15.
LCM of 24 and 15LCM of 24 and 15 = 2 × 2 × 2 × 3 × 5 = 120
LCM of Two Numbers
Suppose there are two numbers, 8 and 12, whose LCM we need to find. Let us write the multiples of these two numbers.
8 = 16, 24, 32, 40, 48, 56, …
12 = 24, 36, 48, 60, 72, 84,…
You can see, the least common multiple or the smallest common multiple of two numbers, 8 and 12 is 24.
HCF and LCM Formula
The formula which involves both HCF and LCM is:
Product of Two numbers = (HCF of the two numbers) x (LCM of the two numbers)
Say, A and B are the two numbers, then as per the formula;
A x B = H.C.F.(A,B) x L.C.M.(A,B)
We can also write the above formula in terms of HCF and LCM, such as:
H.C.F. of Two numbers = Product of Two numbers/L.C.M of two numbers
&
L.C.M of two numbers = Product of Two numbers/H.C.F. of Two numbers
Related Links
Hcf
Lcm
Properties Of Hcf And Lcm
Relation Between Hcf And Lcm
Lcm Of Two Numbers
How to find HCF and LCM?
Here are the methods we can use to find the HCF and LCM of given numbers.
Prime factorisation method
Division method
Let us learn both the methods one by one.
Prime Factorisation for HCF
Take an example of finding the highest common factor of 144, 104 and 160.
Now let us write the prime factors of 144, 104 and 160.
144 = 2 × 2 × 2 × 2 × 3 × 3
104 = 2 × 2 × 2 × 13
160 = 2 × 2 × 2 × 2 × 2 × 5
The common factors of 144, 104 and 160 are 2 × 2 × 2 = 8
Therefore, HCF (144, 104, 160) = 8
Answer:
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