Question

1) The product of two numbers is 12 and 8. Their HCF is 2. Find their LCM.

2) For 2 numbers , the LCM is 5175 and their HCF is 25. Find the product of these numbers.

3) Prove that the following equation is correct- LCM * HCF = PRODUCT OF THE NUMBERS. (Choose any two numbers)

Answer 1

Step-by-step explanation:

a = first number

b = second number

a * b = HCF * LCM

1) 12 * 8 = 2 * LCM

=> LCM = 12 * 8 / 2 = 48

2) a * b = HCF * LCM

=> a * b = 25 * 5175 = 129375

3) Proof using examples:

Let's a = 12 and b = 8

12 = 2 * 2 * 3

8 = 2 * 2 * 2

HCF(12, 8) = 2 * 2 = 4

LCM(12, 8) = (2 * 2) * 3 * 2 = 24

HCF(12, 8) * LCM(12, 8) = 4 * 24 = 96

a * b = 12 * 8 = 96

HCF(12, 8) * LCM(12, 8) = a * b