LCM and HCF

LCM (Least Common Multiple)

The smallest multiple that is exactly divisible by two or more numbers.

HCF (Highest Common Factor)

The largest factor that divides two or more numbers without leaving a remainder.

How do you find the LCM of two numbers?

List the multiples of all the numbers and find the smallest one that appears in all lists.

Example of LCM for 12 and 15

The LCM of 12 and 15 is 60, as it is the smallest multiple common to both lists.

How do you find the HCF of two numbers?

Identify the largest number that exactly divides both values without leaving a remainder.

Example of HCF for 12 and 15

The HCF of 12 and 15 is 3, as it is the largest common factor.

What is the method to find the HCF of multiple numbers such as 36, 54, and 72?

List the factors of each number and determine the highest common factor among them.

Common factors of 36, 54, and 72

The common factors are 1, 2, 3, 6, 9, and 18; thus, the HCF is 18.

Factors of 12

1, 2, 3, 4, 6, 12.

Factors of 15

1, 3, 5, 15.

Prime factorization of 12

2^2 × 3.

Prime factorization of 14

2 × 7.

Prime factorization of 21

3 × 7.

What is the LCM of 12, 14, and 21?

The LCM is 84, calculated by multiplying the highest power of each prime factor.

What is the HCF of 36 and 84?

The HCF is 12, found by taking the lowest power of each common prime factor.