Question

the lcm of two numbers is 1600. which of the following cannot be their HCF? 400,100,500,200​

Answer 1

Answer: 500

Step-by-step explanation:

If 500 was the HCF of two numbers x,y suppose , then

500 divides both x and y .

x = 500a , y = 500b for some a,b

also, Product of two numbers = HCF X LCM

500a x 500b = 500 x 1600

500²ab = 500 x 1600

500ab = 1600

5ab = 16

Note that there is no a,b such that 5ab = 16

Why? , Simple because in the LHS 5 divides 5ab , but in the RHS , 5 does not divide 16 , and that is not possible .

So 500 cannot be the HCF  of two numbers , if their LCM is 1600

Hope this helps you .