LCM of 24 and 36 is 72. Then find their HCF 

By MathHelloKitty

Calculate the least common multiple (LCM) of 24 and 36, obtaining 72. Explore the relationship between LCM and fundamental arithmetic principles.

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LCM of 24 and 36 is 72. Then find their HCF

The highest common factor (HCF) of 24 and 36 is 12.

To find the highest common factor (HCF) of two numbers, we can use the relationship between the LCM (Least Common Multiple) and HCF of those numbers.

For two numbers a and b, their product is equal to the product of their HCF and LCM:

a * b = HCF(a, b) * LCM(a, b)

We know that the LCM of 24 and 36 is 72. So, let’s substitute these values:

24 * 36 = HCF(24, 36) * 72

864 = HCF(24, 36) * 72

Now, to find the HCF, we can divide 864 by 72:

HCF(24, 36) = 864 / 72 = 12

So, the highest common factor (HCF) of 24 and 36 is 12.

Least Common Multiple and Highest Common Factor

The least common multiple (LCM) and highest common factor (HCF), also known as greatest common divisor (GCD), are two fundamental concepts in number theory used to analyze sets of numbers.

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  1. Least Common Multiple (LCM): The LCM of two or more integers is the smallest positive integer that is divisible by each of the given integers without leaving a remainder. It is denoted by LCM(a, b), where ‘a’ and ‘b’ are the numbers for which the LCM is being found.

    For example, the LCM of 4 and 6 is 12, because 12 is the smallest positive integer that is divisible by both 4 and 6.

  2. Highest Common Factor (HCF) or Greatest Common Divisor (GCD): The HCF or GCD of two or more integers is the largest positive integer that divides each of the given integers without leaving a remainder. It is denoted by HCF(a, b), where ‘a’ and ‘b’ are the numbers for which the HCF is being found.

    For example, the HCF of 12 and 18 is 6, because 6 is the largest positive integer that divides both 12 and 18 without leaving a remainder.

These concepts are often used in various mathematical problems and are fundamental in understanding the relationships between numbers. They’re also utilized in simplifying fractions, solving equations, and various other mathematical operations.

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Source: Math Hello Kitty
Categories: Math