NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 1: Number System - Problems and Solutions

Question 183

Step 1: Do prime factorisation.

• \(160 = 2 \times 2 \times 2 \times 2 \times 2 \times 5\)
• So, \(160 = 2^5 \times 5\)
• \(170 = 2 \times 5 \times 17\)
• So, \(170 = 2^1 \times 5^1 \times 17^1\)
• \(90 = 2 \times 3 \times 3 \times 5\)
• So, \(90 = 2^1 \times 3^2 \times 5^1\)

Step 2: Pick the highest power of each prime.

• For \(2\): highest is \(2^5\)
• For \(3\): highest is \(3^2\)
• For \(5\): highest is \(5^1\)
• For \(17\): highest is \(17^1\)

Step 3: Write LCM as the product of these.

\(\text{LCM} = 2^5 \times 3^2 \times 5 \times 17\)

Step 4: Multiply step by step.

\(2^5 = 32\)

\(3^2 = 9\)

\(32 \times 9 = 288\)

\(288 \times 5 = 1440\)

\(1440 \times 17 = 1440 \times 10 + 1440 \times 7\)

\(= 14400 + 10080\)

\(= 24480\)

Therefore, \(\text{LCM}(160,170,90) = 24{,}480\).