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Activity Discussion Math How to find LCM and HCF?

• # How to find LCM and HCF?

Posted by on May 8, 2021 at 7:46 am

How to find LCM and HCF?

4 Members · 3 Replies
• 3 Replies
• ### 19 BCS 081

Member
May 8, 2021 at 12:26 pm
0

LCM stands for â€˜Least Common Multipleâ€™. 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, â€¦â€¦

Multiples of 12= 12, 24, 36, 48, 60, 72, 84, â€¦â€¦

Common Multiples= 12, 24, 36, â€¦â€¦.

Least Common Multiple= L(4, 12)= 12

HCF stand for â€˜Highest Common Factorâ€™. 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

• ### Aruja

Member
May 9, 2021 at 2:49 pm
0

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

• ### Jyothi krishna

Member
May 12, 2021 at 11:46 am
0

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 Ã— 2nd number = L.C. M. Ã— 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 â€˜nâ€™ numbers in a set and H.C.F. of any two

numbers is H and L.C.M. of all â€˜nâ€™ numbers is L, then

product of all â€˜nâ€™ numbers is [(H)^n-1Ã—L].

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