How Do You Find HCF And LCM?

Suppose P and Q are two numbers, then. Relation 2: As HCF of co-prime numbers is 1. Therefore we get that the LCM of given co-prime numbers is equal to the product of the numbers. LCM of Co-prime Numbers = Product of The co-prime Numbers.

How Do You Find LCM And HCF Using Prime Factorization?

Using prime factors to find the HCF and LCM:

  1. Numbers can be broken down into prime factors using prime factor trees.
  2. Find the HCF and LCM of 24 and 180.
  3. Cross any numbers used so far off from the products.
  4. To find the LCM, multiply the HCF by all the numbers in the products that have not yet been used.

How Do You Solve HCF And LCM Easily?

The formula that shows the relationship between their LCM and HCF is: LCM (a,b) × HCF (a,b) = a × b. For example, let us take two numbers 12 and 8. Let us use the formula: LCM (12,8) × HCF (12,8) = 12 × 8. The LCM of 12 and 8 is 24; and the HCF of 12 and 8 is 4.

How Do You Solve HCF Problems?

  1. Step 1: Find the prime factors of the given numbers. In this case, the prime factors of 24 = 2 × 2 × 2 × 3, the prime factors of 36 = 2 × 2 × 3 × 3.
  2. Step 2: Multiply the prime factors that are common to both the numbers.
  3. Step 3: Therefore, the HCF of 24 and 36 is 12.

Is HCF Always Greater Than LCM?

LCM means Lowest Common Multiple. HCF means Highest Common Factor. Since multiple are always greater than or equal to the number and factors are always less than or equal to, we can say that multiple will always be bigger than factors and So the LCM is greater than the HCF

What Is An Example Of A LCM Word Problem?

Find the lowest number which is more by 6 to be divided by 25, 40 and 60 exactly. We find the L.C.M. of 25, 40 and 60. Therefore, the required number is 600 + 6 = 606.

What Is The Fastest Way To Calculate HCF?

Step I: Treat the smallest number i.e., 12 as divisor and the bigger number i.e., 18 as dividend. Step II: The remainder 6 becomes the divisor and the divisor 12 becomes the dividend. Step III: Repeat this process till the remainder becomes zero. The last divisor is the H.C.F.

What Is The Properties Of HCF?

(i) The H.C.F. of two or more numbers cannot be greater than any one of them. For example, the H.C.F. of 16, 18 and 24 is 2 which is less than all the given numbers. (ii) If one number is a factor of the other numbers, their H.C.F. will be that smallest number. For example, 8 is the H.C.F. of 8, 32 and 40.

Who Discovered LCM?

 Algorithm, procedure for finding the greatest common divisor (GCD) of two numbers, described by the Greek mathematician Euclid in his Elements (c. 300 bc). The method is computationally efficient and, with minor modifications, is still used by computers.

Why Do We Need HCF And LCM?

L.C.M and H.C.F of two or more numbers help in finding out quick solutions and thus reduce time during examinations. The concept of L.C.M. is important to solve problems related to racetracks, traffic lights, etc.

How Do You Find HCF Short Tricks?

Division Method to find HCF (Shortcut):

  1. Step 1: Divide the larger number by the smaller number.
  2. Step 2: Divisor of step 1 is divided by its remainder.
  3. Step 3: Divisor of step 2 is divided by its remainder.
  4. Step 4: Divisor of the last step is the HCF.
  5. e.g. Find the HCF of 108 and 288.

How Do You Solve HCF LCM Word Problems?

First we find the least common multiple (L.C.M.) of 28, 36 and 45.

  1. Therefore, least common multiple (L.C.M.) of 28, 36 and 45 = 2 × 2 × 3 × 3 × 5 × 7 = 1260.
  2. Therefore, the required number = 1260 - 19 = 1241.
  3. Highest common factor (H.C.F.) of 90 and 162 = 18.
  4. Relationship between H.C.F. and L.C.M.

How Do You Use HCF And LCM In Word Problems?

You can divide any of the numbers given by HCF (41 ¸ 10) and find the remainder to be equal to 1. L.C.M. of 2, 3 and 6 = 6 ; H.C.F. of 5, 10 and 25 = 5. Thus, the LCM of these three fractions will be 6/5.

How Many Types Of HCF And LCM Are There?

The two principal methods which are used to find the LCM (Least Common Multiple) and the HCF (Highest Common Factor) of the numbers are the Prime Factorization Method and Division Method.

Is HCF And GCD Same?

The greatest common divisor (GCD) of two or more numbers is the greatest common factor number that divides them, exactly. It is also called the highest common factor (HCF). For example, the greatest common factor of 15 and 10 is 5, since both the numbers can be divided by 5.

What Is HCF Of Two Numbers?

HCF or highest common factor is the factor of any two or more numbers, which are common among them. Sometimes, it is also called the greatest common factor (GCF) or greatest common divisor (GCD). For example, the HCF of 2 and 4 is 2, because 2 is the number which is common to both 2 and 4.

What Is Factorisation Method Of HCF?

To find the HCF of two numbers 72 and 120 we can use the prime factorization method. In the prime factorization method firstly we need to write all the prime factors of respective numbers and then find the highest common factor among the two. Here we have, Prime factorization of 72 = 2 × 2 × 2 × 3 × 3 or 2.

What Is The Application Of LCM?

Least Common Multiple i.e. LCM is a method to find the minimum common multiple between any two or more numbers. LCM denotes the least value of common factor or multiple of any two integers.

What Is The Formula Of HCF Into LCM?

HCF and LCM of two numbers are related to each other as well as with the given numbers. For any two numbers a and b, HCF (a, b) × LCM (a, b) = a × b.