The greatest number which when divides 989 and 1327 leaves remainder 5 and 7 respectively is

LCM Formula

Let a and b are two given integers. The formula to find the LCM of a & b is given by:

LCM (a, b) = (a × b) /GCD(a, b)

Where GCD (a, b) means Greatest Common Divisor or Highest Common Factor of a & b.

LCM Formula for Fractions

The formula to find the LCM of fractions is given by:

L.C.M.=L.C.M Of NumeratorH.C.F Of Denominator 

Properties of LCM

LCM By Prime Factorisation

Another method to find the LCM of the given numbers is prime factorization. Suppose, there are three numbers 12, 16 and 24. Let us write the prime factors of all three numbers individually.

12=2×2×3

16=2×2×2×2

24=2×2×2×3

Now writing the prime factors of all the three numbers together, we get;

12×16 ×24=2 × 2 × 3 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3

Now pairing the common prime factors we get the LCM. Hence, there are four 2’s and one 3. So the LCM of 12, 16 and 24 will be;
LCM

(12, 16, 24)=2×2×2×2×3=48

LCM By Division Method

Finding LCM of two numbers by division method is an easy method. Below are the steps to find the LCM by division method:

1. First, write the numbers, separated by commas

2. Now divide the numbers, with the smallest prime number.

3. If any number is not divisible, then write down that number and proceed further

4. Keep on dividing the row of numbers by prime numbers, unless we get the results as 1 in the complete row

5. Now LCM of the numbers will equal to the product of all the prime numbers we obtained in division method

Highest Common Factor(HCF)

1. Highest Common Factor(HCF) of two or more numbers is the greatest number which divides each of them exactly.
2. Greatest Common Measure(GCM) and Greatest Common Divisor(GCD) are the other terms used to refer HCF.

3. Example : HCF of 60 and 75=15 because 15 is the highest number which divides both 60 and 75 exactly.

How To Find HCF By Prime Factorization?

The prime factorization method is also called the factor tree method. Let us understand how to find out HCF using this method with an example:

Step 1: Write each number as a product of its prime factors.

Step 2: Now list the common factors of both the numbers.

Step 3: The product of all common prime factors is the HCF (use the lower power of each common factor).

HCF By Division Method

Step 1: Write the given numbers horizontally, by separating them with commas.

Step 2: Find the smallest prime number which can divide the given numbers. The remainder should be 0 on dividing those numbers by that small number (write on the left side).

Step 3: Now write the quotients.

Step 4: Repeat the process, until you reach the stage, where there is no prime number that can divide all the numbers exactly.

Step 5: Write down all the common prime factors on the left side. The product of these common prime factors is the HCF of the given numbers.

Shortcut Method To Find The HCF Of Two Numbers

There is a shortcut method to find the GCD of numbers quickly. The step-by-step process on how to find HCF quickly is explained below:

Step 1: Divide the larger number by the smaller number first.

Step 2: Divide the divisor of step 1 by the remainder left.

Step 3: Again divide the divisor of step 2 by the remainder.

Step 4: Repeat the process until the remainder is zero.

Step 5: The divisor of the last step is the HCF.

How To Find The HCF Of 3 Numbers?

We have explained how to find the highest common factor of three numbers by using the long division method. The step-by-step process is listed below:

Step 1: Calculate the HCF of the first 2 numbers.

Step 2: Find the HCF of the 3rd number and the HCF found in Step 1.

Step 3: The HCF you got in Step 2 will be the HCF of the given 3 numbers.

LCM And HCF Formula

Product of two numbers = (HCF of the two numbers) × (LCM of the two numbers)
HCF of two numbers = Product of two numbers/LCM of two numbers
LCM of two numbers = Product of two numbers/HCF of two numbers

Properties Of HCF And LCM

Some important properties of HCF and LCM are as under:

1. The HCF of given numbers is never greater or more than any of the numbers.

2. The LCM of given numbers is never less than any of the numbers.

3. The HCF of two or more prime numbers is always 1.

4. The LCM of two or more prime numbers is their product.

5. The product of two numbers, a and b, is equal to the product of their HCF and LCM. It is also known as LCM and HCF formula discussed above.

6. We use the following formulas to calculate the HCF and LCM of fractions.

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