The product of LCM and HCF of any two numbers is equal to the product of the numbers. (a) True (b) False

By Ritesh|Updated : November 14th, 2022

The statement “The product of LCM and HCF of any two numbers is equal to the product of the numbers” is true. Any two numbers' LCM and HCF products are equivalent to their own products. Take the numbers 12 and 18 as an illustration.

Finding the highest common factor (HCF) between 12 and 18 is the first step.

12 = 2 × 2 × 3

18 = 2 × 3 × 3

HCF of 12 and 18 = 2 × 3 = 6

Now, the Lowest common multiple (LCM) of 12 and 18 = 2 × 2 × 3 × 3 = 36

By multiplying them we get

HCF × LCM = 6 × 36 = 216

Also 12 × 18 = 216

HCF and LCM of 12 and 18 are therefore equal to 12 and 18, and vice versa.

HCF and LCM

The highest Common Factor is the full name for HCF in mathematics. According to the laws of mathematics, the largest positive integer that divides two or more positive integers without leaving a remainder is known as the greatest common divisor or gcd.

The Least Common Multiple is the full name for LCM in mathematics. The least common multiple, or LCM, of two numbers, such as a and b, is written as LCM in mathematics (a,b). The smallest or least positive integer that is divisible by both a and b are known as the LCM.

Summary:

The product of LCM and HCF of any two numbers is equal to the product of the numbers. (a) True (b) False

The adage "The product of any two numbers is equal to the product of the LCM and HCF of the numbers" is accurate. The equation that incorporates both HCF and LCM is the Product of Two numbers = (HCF of the two numbers) x (LCM of the two numbers).