II. L.C.M./H.C.F.

L. C. M. / H. C. F.

Factor: One number is said to be a factor or measure of another when it divides the other exactly. Thus 6 and 8 are factors of 48.

Multiple: A number is said to be a multiple of another when it is exactly divisible by the other. Thus 48 is a number of 6 and 8.

Least Common Multiple (L. C. M.) : The Least Common Multiple (L.C.M) of two or more given numbers is the least number, which is exactly divisible by each of them.

Thus 20 is a common multiple of 2, 4, 5 and 10.

40 is a common multiple of 2, 4, 5 and 10.

80 is a common multiple of 2, 4, 5 and 10.

but 20 is a Least common multiple of 2, 4, 5 and 10.The Least Common Multiple is otherwise known as the Lowest Common Multiple.

Highest Common Factor (H. C. F.) = The Highest Common Factor (H. C. F.) of two or more numbers is the Greatest number which divides each of them exactly. Thus 9 is the Highest Common Factor of 18 and 27.The H.C.F is also called as Greatest Common Measure (G.C.M) and Highest Common Divisor (H.C.D)

For any two positive numbers A and B, we have

A x B = (L.C.M of A and B) x (H.C.F of A and B)

If only the LC.M and the H.C.F.’s of two positive numbers are given, we can determine all possible pairs of the two numbers, which satisfy the criteria of L.C.M. and H.C.F. An example to illustrate this is given later.

The formulae to determine L.C.M and H.C.F of fractions are given as

Provided that the given fractions are first converted into their “basic” form. A “basic” form means that there should be no common factor in the numerator and denominator of a given fraction. Thus, a fraction, say , when expressed in its “basic” form, yields .

H.C.F: H.C.F of a set of numbers is the greatest one that will divide those numbers exactly.

L.C.M: L.C.M of a set of numbers is the number, which is the smallest and is divisible by all the numbers.