Question

if x=hcf (a,b) and y=lcm (a,b) find xy if a and b are co - prime numbers

Answer 1

Answer: xy = ab

Step-by-step explanation:

Given: We are given that HCF(a , b) = x, LCM(a , b) = y

To find: According to the question, we need to find the value of xy, if a and b are co - primes.

Solution:

Co - primes are the pair of numbers, whose HCF is 1 and LCM is their product.

→ HCF(a , b) = 1 , LCM(a , b) = a × b

→ x = 1 , y = a × b

On substituting the values in xy,

⇒ xy = 1 × (a × b)

⇒ xy = ab

Hence, xy = ab.

Alternative method:

We know that, product of HCF and LCM of two numbers is equal to product of their numbers.

→ HCF(a , b) × LCM(a , b) = a × b

→ x × y = a × b

→ xy = ab

Final Answer: The value of xy is ab.

# Learn More:

1. The hcf of two numbers is 145 and their lcm is 2175 , if one of the numbers is 725 find the other number

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