Question

What is the least common denominator of the fractions (4)/(35),(1)/(28), and (3)/(8)? A. 40 B. 280 C. 980 D. 1,120 E. 7,840 J. 84 K. 105

Answer 1

Answer: 280 (choice B)

Step-by-step explanation

The LCD is the LCM of the denominators.

One approach to find the LCM is to first list the prime factorization of each value.

• 35 = 5*7
• 28 = 2*2*7
• 8 = 2*2*2

The unique primes are 2, 5, and 7.

• The prime "2" shows up at most three times. This makes 2^3 = 8 to be a factor of the LCM.
• The prime "5" shows up at most one time. Therefore, 5 is also a factor of the LCM.
• The prime "7" shows up once. This makes 7 a factor of the LCM.

The LCM is the product of those values mentioned: 8*5*7 = 40*7 = 280 is the answer.