It is proved that the least common multiple of the n power of a and the n power of B is equal to the n power of the least common multiple of a and B Like the title,

It is proved that the least common multiple of the n power of a and the n power of B is equal to the n power of the least common multiple of a and B Like the title,

Proof: suppose a = Mn
B = QN (n is the greatest common divisor of a and b)
Then, the least common multiple is mnq
a^n=M^2N^2
b^2=Q^2N^2
Obviously: m and Q are prime, so m ^ 2 and Q ^ 2 are prime!
So the least common multiple of a ^ 2 and B ^ 2 is:
M^2N^2Q^2=(MNQ)^2
Get it!

If a = 2 * 3 * n to the second power and B = 3 * n to the third power (n is prime), then the greatest common factor of AB is () the smallest

The greatest common factor of AB is (the second power of 3 * n) and the least common multiple is (the third power of 6 * n)

A = 2 × 3 × N2, B = 3 × N3 × 5, (n is prime), then the greatest common divisor of a and B is______ The least common multiple is______ ．

A = 2 × 3 × N2, B = 3 × N3 × 5 (n is prime), so the greatest common divisor of a and B is 3 × N2; the least common multiple of a and B is 2 × 3 × N3 × 5; so the answer is: 3 × N2, 2 × 3 × N3 × 5