Discussion

(LCM of 96, 120 and 160) ÷ (HCF of 72 and 168) is equal to

Answer: C

The value is 20.

Factorise: \(96 = 2^{5} \times 3\), \(120 = 2^{3} \times 3 \times 5\), \(160 = 2^{5} \times 5\). The LCM takes the highest power of each prime:

\[ \text{LCM} = 2^{5} \times 3 \times 5 = 480 \]

For the HCF, \(72 = 2^{3} \times 3^{2}\) and \(168 = 2^{3} \times 3 \times 7\), and the common part is

\[ \text{HCF} = 2^{3} \times 3 = 24 \]

\[ 480 \div 24 = 20 \]

Option 1 (12) would be 480 divided by 40 and option 4 (30) is 480 divided by 16, the results of mistaken HCFs.

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