Knowee
Questions
Features
Study Tools

If two positive integers a and b are written as a = x3y2 and b = xy3, where x, y are primenumbers, then the result obtained by dividing the product of the positive integers by theLCM (a, b) is

Question

If two positive integers a and b are written as a = x3y2 and b = xy3, where x, y are primenumbers, then the result obtained by dividing the product of the positive integers by theLCM (a, b) is

🧐 Not the exact question you are looking for?Go ask a question

Solution

The problem can be solved in the following steps:

Step 1: Write down the given expressions for a and b. a = x^3 * y^2 b = x * y^3

Step 2: Calculate the product of a and b. a * b = x^3 * y^2 * x * y^3 = x^4 * y^5

Step 3: Calculate the least common multiple (LCM) of a and b. The LCM of two numbers is the product of the highest powers of all primes appearing in the factorization of the numbers. So, LCM(a, b) = x^3 * y^3

Step 4: Divide the product of a and b by the LCM of a and b. (x^4 * y^5) / (x^3 * y^3) = x * y^2

So, the result obtained by dividing the product of the positive integers a and b by the LCM(a, b) is x * y^2.

This problem has been solved

Similar Questions

If two positive integers a and b are written asa = x3y2 and b = xy3 ; x, y are prime numbers, then HCF (a, b) is

If two positive integers p and q can be expressed as p = ab2 and q = a3b ;   a, b being prime numbers, then LCM (p, q) isaba2b2a3b2a3b3

1. If two positive integers a and b are written as a = x3y2 and b = xy3; where x, y are prime numbers, then HCF (a,b) is: a) xy b) xy2 c) x3y3 d) x2y2

The lcm of two prime numbers a and b is _________  a/baba+b1

Let a and b be two positive integers such that a = p3q4 and b = p2q3 , where p and q areprime numbers. If HCF(a,b) = pmqn and LCM(a,b) = prqs, then (m+n)(r+s

1/2

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.