Mathematical solution of greatest common divisor and least common multiple

Multiply each number by prime factors such as 2, 3, 5 and 7 (natural numbers that cannot be decomposed into other two positive integers), and the greatest common divisor is the product of the same prime factor; The least common multiple is the product of the same time and all other prime factors.

For example: 40=2*2*2*5

30=2*3*5

Maximum common divisor: both formulas have 2 and 5, and all the maximum common divisors are 2*5= 10.

Least common multiple: 2 and 5 are taken only once, others are 2, 2 and 3; All the least common multiples are 2*5*2*2*3= 120.