Highest Common Factor And Least Common Multiple of two or more numbers
Why are H.C.F and L.C.M important?
The chapter of H.C.F and L.C.M is very important. This concept is useful in the chapters of time and distance, time and work, pipes and cisterns, etc. The tricks used to find
L.C.M and H.C.F of two or more numbers help in finding out quick solutions and thus reduce time during exams.
L.C.M. concept is important to solve problems related to racetracks, traffic lights, etc.
H.C.F. concept is useful in calculating the largest size of tile/room in particular area, largest tape to measure the land, etc.
Important terms
1) Factors: Factor is a number which exactly divides other number.
Example: 3 and 5 are factors of 15
2) Multiple: A number is said to be multiple of another number when it is exactly divisible by another number.
Example: 15 is a multiple of 3 and 5
3) Common multiple: A common multiple of two or more numbers is a number which is exactly divisible by each of them.
Example: 18 is a common multiple of 2,3,6 and 9
4) H.C.F/G.C.F:M/b> (Highest Common Factor / Greatest Common Factor). H.C.F of two or more numbers is the greatest number which divides each number exactly.
5) L.C.M.: (Lowest common multiple). The least number exactly divisible by each one of the given numbers is called least common multiple.
Points To Remember
Before studying this chapter, make sure that the basic concepts of numbers (prime numbers, composite numbers, co-prime numbers, etc) are perfectly understood. Knowing basics will help in understanding this chapter.
Quick Revision of prime numbers, composite numbers and co-prime numbers is given below