Find LCM of 80, 96, 125, 160.
LCM = 2400
Step 1: Write prime factors
\(80 = 2\times 2\times 2\times 2\times 5\)
\(\quad\;= 2^{4}\times 5\)
\(96 = 2\times 2\times 2\times 2\times 2\times 3\)
\(\quad\;= 2^{5}\times 3\)
\(125 = 5\times 5\times 5\)
\(\quad\;= 5^{3}\)
\(160 = 2\times 2\times 2\times 2\times 2\times 5\)
\(\quad\;= 2^{5}\times 5\)
Step 2: Take highest powers of each prime
Prime \(2:\;\max(2^{4}, 2^{5}, -, 2^{5}) = 2^{5}\)
Prime \(3:\;\max(-, 3^{1}, -, -) = 3^{1}\)
Prime \(5:\;\max(5^{1}, -, 5^{3}, 5^{1}) = 5^{3}\)
Step 3: Form the LCM
\(\text{LCM} = 2^{5}\times 3^{1}\times 5^{3}\)
Step 4: Multiply step by step
\(2^{5} = 32\)
\(5^{3} = 125\)
\(32 \times 3 = 96\)
\(96 \times 125 = 12000\)
Therefore, \(\text{LCM} = 12000\).