Find the number of common prime factors in the decomposition of the numbers GCD (15; 30)

Find the number of common prime factors in the decomposition of the numbers GCD (15; 30) and LCM (9; 18) into prime factors.

1. Let’s decompose the numbers into prime factors:
15 = 1 * 3 * 5.
30 = 1 * 2 * 3 * 5.
2.Let’s find the common factors of the entered numbers: 3 5.
GCD is equal to the product of the found factors:
GCD = 1 * 3 * 5 = 15.
3. Let’s write out all the factors of the entered numbers, except for those found earlier: 2 3 5.
The LCM is equal to the product of these factors:
LCM = 1 * 2 * 3 * 5 = 15.
Also, the NOC can be found in another way:
LCM = N1 * N2 / GCD = 15 * 30/15 = 30.
1. Let’s decompose the numbers into prime factors:
9 = 1 * 3 * 3.
18 = 1 * 2 * 3 * 3.
2.Let’s find the common factors of the entered numbers: 3 3.
GCD is equal to the product of the found factors:
GCD = 1 * 3 * 3 = 9.
3. Let’s write out all the factors of the entered numbers, except for those found earlier: 2 3 3.
The LCM is equal to the product of these factors:
LCM = 1 * 2 * 3 * 3 = 9.
Also, the NOC can be found in another way:
LCM = N1 * N2 / GCD = 9 * 18/9 = 18.