Question

If a and b are two positive numbers the gcd then gcd (a.b)=? If it known that lcm (a,b)=16 and ab=64

Answer 1

Answer:64

Step-by-step explanation:

according to a theorem

Product of no.s is=product of their lcm and hcf

=>ab=lcm*hcf

=>64=16*ab=>ab=64/16=4

plz mark it brainliest

Answer 2

Answer:

The value of GCD(ab) is 4.

Explanation:

Let's first find the values of a and b using the given information:

We know that lcm(a, b) × gcd(a, b) = a × b

Substituting lcm(a, b) = 16 and ab = 64, we get:

16 × gcd(a, b) = 64

gcd(a, b) = 4

Now, we can use the formula gcd(a, b) × lcm(a, b) = a × b to find the value of ab/gcd(a, b):

4 × 16 = a × b

ab = 64

So, we have a = 8 and b = 8.

Therefore, gcd(a, b) = gcd(8, 8) = 8.

Hence, gcd(a.b) = gcd(8.8) = 8.

We can use the following formula relating the GCD and LCM of two numbers:

GCD(a, b) * LCM(a, b) = a * b

Given that LCM(a, b) = 16 and ab = 64, we can solve for GCD(a, b) as follows:

GCD(a, b) * 16 = 64

GCD(a, b) = 64 / 16

GCD(a, b) = 4

Therefore, GCD(ab) = 4.

To learn more about similar question visit:

https://brainly.in/question/20979832?referrer=searchResults

https://brainly.in/question/39286910?referrer=searchResults

#SPJ3