Question

find the pair of numbers below with a greatest common factor of 8 and a least common multiple of 120.

answer

○ 40, 56
○ 16, 24
○ 24, 40
○ 3, 120

Explanation:

Step1: Recall GCF and LCM formulas

For two numbers \(a\) and \(b\), we know that \(\text{GCF}(a,b) \times \text{LCM}(a,b)=a\times b\). Also, we can find GCF by prime factorization.

Step2: Check each option

• Option 40, 56:

Prime factors of \(40 = 2^3\times5\), \(56 = 2^3\times7\). GCF is \(2^3 = 8\). LCM: \(\frac{40\times56}{8}=\frac{2240}{8} = 280
eq120\). So this is wrong.

• Option 16, 24:

Prime factors of \(16 = 2^4\), \(24 = 2^3\times3\). GCF is \(2^3 = 8\). LCM: \(\frac{16\times24}{8}=\frac{384}{8}=48
eq120\). Wrong.

• Option 24, 40:

Prime factors of \(24 = 2^3\times3\), \(40 = 2^3\times5\). GCF is \(2^3 = 8\). LCM: \(\frac{24\times40}{8}=\frac{960}{8}=120\). Correct.

• Option 3, 120:

GCF of 3 and 120 is 3 (since 3 is prime and \(120\div3 = 40\)), not 8. Wrong.

Answer:

C. 24, 40 (assuming the options are labeled as A. 40, 56; B. 16, 24; C. 24, 40; D. 3, 120)