Problem Statement
Find the LCM of 12 and 18.
Explanation
LCM or Lowest Common Multiple is the smallest number that is a multiple of both numbers. We can use prime factorization or the relationship between HCF and LCM.
Prime factorization: 12 equals 2 squared times 3. 18 equals 2 times 3 squared. LCM equals product of all prime factors with highest powers equals 2 squared times 3 squared equals 4 times 9 equals 36. Using relationship: LCM times HCF equals product of numbers. LCM equals 12 times 18 divided by HCF equals 216 divided by 6 equals 36.
Code Solution
SolutionRead Only
// Method 1: Prime Factorization // 12 = 2² × 3¹ // 18 = 2¹ × 3² // LCM = 2² × 3² = 4 × 9 = 36 // Method 2: Using HCF // LCM × HCF = Product of numbers // LCM = (12 × 18) / HCF // LCM = 216 / 6 = 36 // Verification: // Multiples of 12: 12, 24, 36, 48... // Multiples of 18: 18, 36, 54... // First common: 36
Practice Sets
This question appears in the following practice sets:
