Highest Common Factor(HCF)
Highest Common Factor(HCF) of two or more numbers is the greatest number which divides each of them exactly.Greatest Common Measure(GCM) and Greatest Common Divisor(GCD) are the other terms used to refer HCF.
Example : HCF of 60 and 75 = 15 because 15 is the highest number which divides both 60 and 75 exactly.
We can find out HCF using prime factorization method or by dividing the numbers or division method.
Least Common Multiple (L.C.M.)
The least number which is exactly divisible by each one of the given numbers is called their L.C.M.
There are two methods of finding the L.C.M. of a given set of numbers:
1. Factorization Method,
2. Division Method (Division Method is short cut method of LCM)1. Factorization Method: Resolve each one of the given numbers into a product of prime factors. Then, L.C.M. is the product of highest powers of all the factors.
2. Division Method : Arrange the given numbers in a row in any order. Divide by a number which divided exactly at least two of the given numbers and carry forward the numbers which are not divisible. Repeat the above process till no two of the numbers are divisible by the same number except 1. The product of the divisors and the undivided numbers is the required L.C.M. of the given numbers.
Q Find the LCM of 6,9, 12, 15 and 18.
a) 180
b) 360
c) 90
d) 270
Q. Find the LCM of 0.32, 0.4 and 0.002.
a) 1.6
b) 0.32
c) 0.4
d) 0.04
Q.What will be the HCF of 3/4, 4/5 and 7/60?
a) 1/60
b) 84
c) 1
d) 3