Real-Life Example Of HCF and LCM

Various real-life examples of HCF and LCM are added below:

Buying Tiles For a Room

Aditya wants to tile the floor of his living room and bedroom with square tiles. The living room measures 30 feet by 40 feet, while the bedroom measures 60 feet by 80 feet.

• Living Room: Aditya wants to buy square tiles that perfectly fit the dimensions of his living room. He needs to find the size of the tiles that will evenly cover the floor without any gaps.

• Bedroom: Similarly, Aditya wants to buy square tiles for his bedroom, ensuring they fit the dimensions of the room perfectly without any leftover spaces.

Finding HCF: The HCF of the dimensions of both rooms (30 and 60) is 30. This means that the largest square tile that can evenly fit both the living room and the bedroom without any gaps is 30 feet by 30 feet.

Finding LCM: The LCM of the dimensions of both rooms (30 and 60) is 60. This means that if Aditya buys square tiles with dimensions of 60 feet by 60 feet, he’ll have enough to cover both the living room and the bedroom without any leftover tiles.

So, in this real-life scenario, the HCF helps determine the largest tile size that can evenly fit both rooms, while the LCM helps calculate the total quantity needed to cover both rooms without any leftover tiles.

Relationship Between LCM and HCF

Product Relationship: If you multiply the LCM (Least Common Multiple) and the HCF (Highest Common Factor) of any two numbers together, you get the product of those two numbers. For example, if you have two numbers, let’s say 4 and 6, then LCM(4,6) × HCF(4,6) = 4 × 6.

Co-Prime Numbers: When you have co-prime numbers (numbers with no common factors other than 1), their HCF is always 1. So, for co-prime numbers, the LCM is equal to the product of the numbers themselves.

Least Common Multiple (LCM) is the smallest number that can be evenly divided by two or more given numbers. Whereas Highest Common Factor (HCF) is the largest number that can evenly divide two or more given numbers.

LCM and HCF can be easily found using two main methods:

• Division Method
• Prime Factorization Method

In this article, we will learn about HCF and LCM Definition, application of HCF and LCM and others in detail.