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