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------------------------------------------------ If A is the least common multiple of 12, 24, and 36, and B is the lowest prime number, what is the sum of A and B?

F. 3
G. 4
H. 73
J. 74
K. 145

Answer :

Answer:

74

Step-by-step explanation:

A= Least common multiple of 12,24,36

Factors of 12 = 2*2*3

Factors of 24 = 2*2*2*3

Factors of 36 = 2*2*3*3

A = 2*2*2*3*3 = 72

B = Lowest prime number = 2

A+B = 72+2 = 74

The least common multiple of 12, 24, and 36 is 72, and the lowest prime number is 2, making their sum 74. Therefore, the correct answer is J. 74.

To find the sum of A and B, we need to determine the least common multiple (LCM) of 12, 24, and 36, and the lowest prime number.

  1. List the prime factorization of each number:
    12 = 2² x 3
    24 = 2³ x 3
    36 = 2² x 3²
  2. Identify the highest powers of each prime:
    2³ from 24
    3² from 36
  3. Calculate the LCM by multiplying these highest powers:
    LCM = 2³ x 3² = 8 x 9 = 72
  4. The lowest prime number is 2.
  5. Sum A and B:
    A = 72
    B = 2
    A + B = 72 + 2 = 74

So, the correct answer is J. 74.

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