Find the least number which when divided by 25, 40 and 60 leaves 9 as the remainder in each case
Answers
Answer:25, 40, and 60 exactly divides the least number that is equal to their LCM.
Step-by-step explanation:So, the required number that leaves 9 as a remainder will be LCM + 9.
Answer is given in above pic⤴️
More information about H.CF and L.C.M:
HCF and LCM: Basic Arithmetic plays a vital role in laying a strong foundation of Mathematics, a subject that is dreaded by many. With your concepts clear right from the beginning, you won’t face any difficulty in understanding the various advanced concepts that are taught in higher classes. Highest Common Factor and Lowest Common Multiple or HCF and LCM, in short, are two such concepts that find importance not only for school-level Mathematics but also in various other exams, like CAT, MAT, recruitment exams for government jobs, etc. It is, therefore, important that you understand the properties of HCF and LCM properly.
We use Prime Factorisation and Division method to find the HCF & LCM of two or more numbers. In this article, we will explain what are HCF and LCM, their definition, LCM and HCF full form, the relationship between LCM and HCF, properties, along with formulas related to HCF and LCM, and solved examples.
HCF And LCM Definition
Let us first look at the definition of both LCM and HCF:
What is HCF?: The greatest common factor (GCF or GCD or HCF) of a set of whole numbers is the largest positive integer that divides evenly all the given numbers with zero remainders. HCF stands for Highest Common Factor. HCF is also known as GCF (Greatest Common Factor) or GCD (Greatest Common Divisor). Now you know the full form of HCF.
What is a “Factor”?: Factors of a number are numbers that divide the given number exactly without leaving any remainder. That is, they are exact divisors of the given numbers. For example, the number 12 is divisible by 2, 3, 4, and 6.
The Highest Common Factor of two or more numbers is the highest number by which all the given numbers are divisible without leaving any remainders. Basically, it is the largest number that divides all the given numbers.
What is LCM?
LCM stands for Lowest or Least Common Multiple. The LCM of two or more numbers is the smallest positive integer that is divisible by all the given numbers.
Let’s understand the concept of LCM with an example:
Consider two numbers: 8 and 12.
The multiples of 8 are:
8 X 1 = 8,
8 X 2 = 16,
8 X 3 = 24,
8 X 4 = 32, and so on…
The multiples of 12 are:
12 X 1 = 12,
12 X 2 = 24,
12 X 3 = 36,
12 X 4 = 48, and so on…
Of all these multiples of 8 and 12, 24 is the lowest and common multiple of both. So, 24 is the LCM of 8 and 12.
