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) is
Question
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) is
Solution
The LCM (Least Common Multiple) of two numbers is the smallest number that is a multiple of both.
Given that p = ab² and q = a³b, where a and b are prime numbers, we can find the LCM by taking the highest powers of all primes in the given numbers.
In p = ab², the powers of a and b are 1 and 2 respectively. In q = a³b, the powers of a and b are 3 and 1 respectively.
The highest power of a in both p and q is 3 (from q = a³b) and the highest power of b in both p and q is 2 (from p = ab²).
Therefore, the LCM of p and q is a³b².
Similar Questions
If two positive integers p and q can be expressed as p=ab^ 2 \& q = a ^ 3 * b where a, b being prime numbers then LCM (p, q) is equal to a. ab b. a ^ 2 * b ^ 2 c. a ^ 3 * b ^ 2 d. a ^ 2 * b ^ 3
The lcm of two prime numbers a and b is _________
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
If a, b are integers such that a > b then lcm(a, b) lies in _________ a>lcm(a, b)>b a>b>lcm(a, b) lcm(a, b)>=a>b none of the mentioned
If p and q are two coprime numbers, then p3 and q3 are?
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.