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How to find LCM and HCF?
How to find LCM and HCF?
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3 Replies
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LCM stands for ‘Least Common Multiple’. It is thus the smallest number which gets exactly divisible by the given two or more numbers. If we had to find the then LCM of two numbers say a and b. Then L(a,b) is the least positive integer which gets divisible by both a and b.
For example:- Find the LCM of 4 and 12.
Solution:-
Multiples of 4= 4, 8, 12,16, 20, 24, 28, 32, 36, ……
Multiples of 12= 12, 24, 36, 48, 60, 72, 84, ……
Common Multiples= 12, 24, 36, …….
Least Common Multiple= L(4, 12)= 12
HCF stand for ‘Highest Common Factor’. Hence, it is the greatest factor that exists between given two or more than two numbers. Or as we may say, it is the highest positive integer H(a, b) dividing two or more than two numbers (here, a and b) without leaving any remainder.
For example:- Find the HCF of 144 and 104.
Solution:-
Factors of 144= 2 x 2 x 2 x 2 x 3 x 3
Factors of 104= 2 x 2 x 2 x 13
Highest Common Factor= H(144, 104)= 2 x 2 x 2 = 8
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Full Form of LCM is ‘ Least common multiple’.
That means the smallest number (C) that can be divided by both given integers in the question (a,b). The LCM of two number comes when we take out the smallest common multiple from the tables of the two given numbers in the question.
Example- Find the LCM of 8, 16
so first we will take out the factor of
8= 8, 16, 24, 32, 40, 48,…..
16= 16, 32, 48,……
The common multiple that we get from both the tables is 16.
Ans) LCM of (8,16)= 16
Full Form of HCF is ‘ Highest Common Factor ‘.
That means the highest common factor basically the number which can divide both the number leaving number in denominator or which completely divide without leaving a remainder. It comes when we pick as many common numbers from both the numbers factors.
Example- Find HCF of 6,16
Factors of 6= 2 * 3
Factors of 16= 2 * 2 * 2 * 2
Now we will pick the common number from both of the factor = 2.
So HCF of (6,16)= 2
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Highest Common Factor (H.C.F) : It is also called
Greatest common Diviser (G.C.D). When a greatest number
divides perfectly the two or more given numbers then that
number is called the H.C.F. of two or more given numbers.
e.g.
The H.C.F of 10, 20, 30 is 10 as they are perfectly
divided by 10,5 and 2 and 10 is highest or greatest of
them.
Least common Multiple (L.C.M.) : The least number
which is divisible by two or more given numbers, that least
number is called L.C.M. of the numbers.
L.C.M. of 3,5,6 is 30, because all 3 numbers divide
30, 60, 90, …… and so on perfectly and 30 is minimum of
them.
Factor and Multiple : If a number m, divides perfectly
second number n, then m is called the factor of n and n is
called the multiple of m.
Rule 1 : 1st number × 2nd number = L.C. M. × H.C.F.
l There are two methods for calculating the H.C.F
and L.C.M.
(i) Factor Method
(ii) Division Method
l If the ratio of two numbers is a:b, (lowest form i.e.
indivisible to each other) then
Numbers are ak and bk, where k is a constant and
hence,
H.C.F. is K and L.C.M. is abk
Rule 2 :
L.C.M of fractions=L.C.M.of numerators/
H.C.F.of denominators
Rule 3 :
H.C.F. of fractions=H.C.F of numerators/
L.C.M.of denominators
l If there is no common factor between two numbers,
then L.C.M. will be the product of both numbers.
l If there are ‘n’ numbers in a set and H.C.F. of any two
numbers is H and L.C.M. of all ‘n’ numbers is L, then
product of all ‘n’ numbers is [(H)^n-1×L].
