Question

find the LCM by Prime factorization
(a)24,36 (b)16,48
(c) 28, 32, 64 (d) 60,72,96.​

Answer 1

a.) The prime factorization of 24 is: 2 x 2 x 2 x 3. The prime factorization of 36 is: 2 x 2 x 3 x 3. The prime factors and multiplicities 24 and 36 have in common are: 2 x 2 x 3.

b.) the factors and prime factorization of 16 and 48. The biggest common factor number is the GCF number. So the greatest common factor 16 and 48 is 16.

c). The factors of 28 are:

1, 2, 4, 7, 14, 28

The factors of 32 are:

1, 2, 4, 8, 16, 32

The factors of 64 are:

1, 2, 4, 8, 16, 32, 64

The common factors are:

1, 2, 4

The Greatest Common Factor:

GCF = 4

d.) The factors of 60 are:

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

The factors of 72 are:

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

The factors of 96 are:

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

The common factors are:

1, 2, 3, 4, 6, 12

The Greatest Common Factor:

GCF = 12