If hcf and lcm of two numbers are 12 and 396 respectively and one number is 36 find the other number

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NUMBER SYSTEM

1. Natural numbers: These are the numbers (1, 2, 3, etc.) that are used for counting.
2. Whole numbers: The set of numbers that includes all natural numbers and the number zero are called whole numbers. Whole numbers are also called as Non-negative integers.
3. Prime numbers: A natural number larger than 1 is a prime number if it does not have other divisors except for itself and 1. (The lowest prime number is 2. 2 is also the only even prime number. The lowest odd prime number is 3.)
4. Composite numbers: It is a natural number that has at least one divisor different from unity and itself.
5. Even numbers: An even number is an integer that can be divided by two and remain an integer or has no remainder.
6. Odd numbers: An integer that is not an even number is an odd number.
7. If the numbers n1 and n2 are exactly divisible by the same number x, then x is a common divisor of n1 and n2. The highest of all the common divisors of n1 and n2 is called as the GCD or the HCF.
8. Co-prime numbers are any two numbers which have an HCF of 1. (Two consecutive natural numbers are always co-prime. Two consecutive odd numbers are always co-prime. Two prime numbers are always co-prime.)
9. HCF of two or more fractions is given by: HCF of numeratorLCM of denominator

10. LCM of two or more fractions is given by:

LCM of numeratorHCF of denominator

11. LCM × HCF = Product of two numbers n1 × n2

12. N = paqbrcpaqbrc, where, p, q and r are prime factors of the number n.
a, b and c are non-negative powers/exponents
Number of factors of N =a + 1b +1c + 1

Number of odd factors will be all possible combinations of powers of odd numbers (excluding any power of 2)

1.Divisibility by 2 or 5: A number is divisible by 2 or 5 if the last digit is divisible by 2 or 5.

2.Divisibility by 3 (or 9): All such numbers the sum of whose digits are divisible by 3 (or 9) are divisible by 3(or 9).

3. Divisibility by 4: A number is divisible by 4 if the last 2 digits are divisible by 4.

4. Divisibility by 6: A number is divisible by 6 if it is simultaneously divisible by 2 and 3.

5.Divisibility by 8: A number is divisible by 8 if the last 3 digits of the number are divisible by 8.

6. Divisibility by 11: A number is divisible by 11 if the difference of the sum of the digits in the odd places and the sum of the digits in the even places is either zero or is divisible by 11.

7. Divisibility by 12: All numbers divisible by 3 and 4 are divisible by 12.

8. Divisibility by 7, 11 or 13: The integer n is divisible by 7, 11 or 13 if and only if the difference of the number of its thousands and the remainder of its division by 1000 is divisible by 7, 11 or 13.
Products:

1. Odd × odd = odd
2. Odd × Even = Even
3. Even × Even = Even

Simplification

1. Simplification questions will be solved by VBODMAS rule.
V = Vinculum
B = Bracket
O = Of or Order

D = Division
M = Multiplication
A = Addition
S = Subtraction

2. To solve the approximation question, convert decimal values to the nearest values (i.e. 123.13=123, 545.18=545).
3. If the questions are based on square/cube and square/cube root, try to convert them into the nearest perfect square/cube number.

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 × bGCDa, b
Where GCDa, 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

Highest Common Factor(HCF)

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

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 numbersLCM of two numbers
LCM of two numbers = Product of two numbersHCF 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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