Finding the LCM and HCF of two or three numbers The Least Common Multiple (LCM) and Highest Common Multiple (HCF) of two or more numbers are the smal...
The Least Common Multiple (LCM) and Highest Common Multiple (HCF) of two or more numbers are the smallest non-negative integers that divide each of the numbers evenly. In simpler terms, it's the smallest number that is a multiple of all the given numbers.
Finding the LCM:
Identify the factors of each number. This means finding all the different positive integers that evenly divide the number. For example, the factors of 12 are 1, 2, 3, 4, and 6.
Find the LCM by multiplying the factors of each number. For 12, the LCM would be 12 itself.
Write down the LCM.
Finding the HCF:
Identify the factors of each number.
Find the HCF by finding the largest number of the factors. This is because the HCF will be the largest number that divides all the numbers evenly. For example, the factors of 12 are 1, 2, 3, 4, and 6, and the largest common factor is 12 itself, which is the HCF of 12, 18, and 24.
Write down the HCF.
Examples:
LCM of 12 and 18: 36
HCF of 36 and 45: 6
LCM of 6 and 12: 12
HCF of 12 and 24: 12
Key points:
The LCM and HCF of two numbers are always positive integers.
The LCM is always greater than the HCF.
The LCM of three or more numbers is the product of the LCMs of the individual pairs of numbers.
The HCF of three or more numbers is the greatest common divisor of the three numbers