Mathematics is never an easy subject to understand, it takes patience and a keen sense of curiosity and appreciation to comprehend it. But at your age, it is easy enough to grasp these concepts. Hence it’s of great importance that one spends enough time on revising and clearing their doubts. With this, we proceed to LCM and HCF. Factors, and multiples must have surely been covered in the previous classes. There is no need to be apprehensive. One only needs to understand the concepts clearly, in time, one will be able to tackle problems related to it quite easily.
HCF – Highest Common Factor:
As has been taught in Factors and multiples, the factors of a number are all the numbers that divide into it. Let’s proceed to the highest common factor (HCF) and the least common multiple (LCM). As the rules of mathematics dictate, the greatest common divisor or the gcd of two or more integers, when at least one of them is not zero, happens to be the largest positive that divides the numbers without a remainder. For instance, take 8 and 12, the gcd of these two numbers or the HCF of two numbers will be 4. Since this greatest common divisor or GCD is also known as the highest common factor or HCF.
LCM- Least Common Multiple:
In arithmetic, the least common multiple or LCM of two numbers , let’s assume a and b, is denoted as LCM (a,b) is the smallest or least, as the name suggests, positive integer that is divisible by both a and b. Take the LCM of 4 and 6. Multiples of four are: 4,8,12,16,20,24 and so on while that of 6 is 6,12,18,24…. The common multiples for four and six are 12,24,36,48…and so on. The least common multiple in that lot would be 12. Let us now try to find out the LCM of 24 and 15.
LCM of 24 and 15 = 2 × 2 × 2 × 3 × 5 = 120
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