Two positive integers m and n are expressed as m=p5q2 and n=p3q4, where p and q are prime numbers. The LCM of m and n is :
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Step-by-Step Solution
Step 1: Understand the problem
We are given two positive integers, m and n, expressed in terms of their prime factors p and q. We need to find their Least Common Multiple (LCM).
Step 2: Recall the LCM formula for prime factorization
To find the LCM of two numbers expressed in their prime factorization, we take each common prime factor raised to the highest power it appears in either factorization. If a prime factor appears in only one number, we include it with its power.
Step 3: Identify prime factors and their powers
For the prime factor p, the powers are 5 in m and 3 in n. The maximum power is 5. For the prime factor q, the powers are 2 in m and 4 in n. The maximum power is 4.
Step 4: Calculate the LCM
Combining the prime factors with their highest powers, the LCM of m and n is p5q4.