Product of LCM and HCF of two numbers is equal to the product of the two numbers. [If A and B are two numbers then AXB=HCF (A, B) X LCM (A,B)] Show the above as true by taking any 3 example.
Answers
Answer:
Let's take three examples to show that the product of LCM and HCF of two numbers is equal to the product of the two numbers.
Example 1: A = 6 and B = 8
HCF (6, 8) = 2
LCM (6, 8) = 24
Product of A and B = 6 x 8 = 48
Product of HCF and LCM = 2 x 24 = 48
Therefore, AXB=HCF (A, B) X LCM (A,B) is true for A = 6 and B = 8.
Example 2: A = 12 and B = 15
HCF (12, 15) = 3
LCM (12, 15) = 60
Product of A and B = 12 x 15 = 180
Product of HCF and LCM = 3 x 60 = 180
Therefore, AXB=HCF (A, B) X LCM (A,B) is true for A = 12 and B = 15.
Example 3: A = 20 and B = 25
HCF (20, 25) = 5
LCM (20, 25) = 100
Product of A and B = 20 x 25 = 500
Product of HCF and LCM = 5 x 100 = 500
Therefore, AXB=HCF (A, B) X LCM (A,B) is true for A = 20 and B = 25.
Hence, we can see that for all three examples, the product of LCM and HCF of two numbers is equal to the product of the two numbers. Therefore, the statement "AXB=HCF (A, B) X LCM (A,B)" is true for any two positive integers A and B.