The Highest Common Factor (HCF)
of two or more given numbers is the highest (or greatest) of their common factors. It is also known as Greatest Common Divisor (GCD).
The HCF of 20, 28 and 36 :
factors of 20 = 2*2*5
factors of 28= 2*2*7
factors of 36 = 2*2*3*3
underlined part is common so 2*2= 4 is HCF
The Lowest Common Multiple (LCM)
of two or more given numbers is the lowest (or smallest or least) of their common multiples.
LCM of 12 and 18.
Solution : prime factorisations of 12 and 18 are :
12=2×2×3
18=2×3×3
take common factor 2*3 , now
highest number of 2 in any digit : 2 times =2*2=4
highest number of 3 in any digit : 2 times =3*3=9
So LCM of 12 & 18 is 4*9=36
Product of two numbers = (HCF * LCM) of two numbers