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**HCF And LCM Formulas:**

**Factor:**

One number is said to be a factor when it divides the other number exactly. Those 3 and 4 are factors of 12.

**Multiple:**

One number is said to be a multiple of another number when it is exactly divisible by other.

**Common Factor:**

A common factor of two or more numbers is a number that divides each of them exactly.

Thus 5 is acommon factor of 10,15,25,45,75

**Highest Common Factor:**

HCF of two or more given numbers is the greatest number that divides of them exactly.

Thus 4 is the HCF of 36 and 48

HCF is also called Highest Common Divisor or Greatest Common Divisor.

HCF of Fractions = HCF of Numerators / LCM of Denominators

**Metods to find LCM:**

A method of prime factors:

Divide the given numbers into their prime factors and then find the product of all the factors of highest powers that occur in the given numbers, and this product wiil be the required LCM.

**Example:**

LCM of 3,6 and 21 is

3= 3 * 1

6 = 3*2*1

21 = 3*7

The prime factors that occur here are 1, the highest powers of these prime factors are 7 and 3 and 2 and 1

Therefore the required LCM is 7 * 3 * 2 * 1 = 42

**Regular Method:**

Write all the given numbers in a line and divide them by a number which will exactly divide at least any two of the numbers. Write down the quotients and then undivided numbers in a line below the first. Repeat the process until we get a line of numbers which are prime to each other. Then the product of all the divisors and the numbers in the last line will be the required LCM.

**Example:**

LCM of 5, 10 and 40

**LCM of decimals:**

First, find the given numbers without decimals and then put the decimal in the result after the number of digits which is equal to the minimum digits after the decimal in the given numbers from right to left.

LCM of Fractions = LCM of NUmerators / HCF of Denominators

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