Answer:
144
Step-by-step explanation:
We know that any integer can be written as a product of prime numbers.
Then if two given numbers share a given amount of prime numbers, then the product of all of these shared prime numbers is the highest common factor between these two numbers:
Here we have:
m = 2⁴*3³
n = 2³*3²*13
We want to find the highest common multiple of 3*m and 2*n, let's write these numbers, and remember that:
a*aⁿ = a⁽ⁿ ⁺ ¹⁾
Then:
3*m = 3*( 2⁴*3³) = 2⁴*3⁴
2*n = 2*( 2³*3²*13) = 2⁴*3²*13
So both of these numbers have the factor 2 four times.
And both of these numbers have the factor 3 at least 2 times.
So we can rewrite:
3*m = 2⁴*3⁴ = (2⁴*3²)*3²
2*n = 2⁴*3²*13 = (2⁴*3²)*13
Then the highest common multiple is:
2⁴*3² = 16*9 = 144
