Question - Finding the Least Common Multiple (LCM) of 66 and 240
Solution:
The question in the image asks to determine the least common multiple (LCM) of 66 and 240.To find the LCM of two numbers, you can use the prime factorization method, where you break down each number into its prime factors and then multiply each factor the greatest number of times it occurs in either number.Let's find the prime factors of each:1. Prime factors of 66:66 = 2 × 3 × 112. Prime factors of 240:240 = 2 × 2 × 2 × 2 × 3 × 5240 = 2^4 × 3 × 5Now, let's find the LCM:The LCM will include all prime factors that appear in either number, taken the greatest number of times they occur in either number's prime factorization.So, we take:- The factor 2: the greatest power of 2 appearing in either factorization is 2^4.- The factor 3: the greatest power of 3 appearing is 3^1 (or just 3).- The factor 5: this only appears in the factorization of 240, so we take it once.- The factor 11: this only appears in the factorization of 66, so we take it once.LCM(66, 240) = 2^4 × 3 × 5 × 11 = 16 × 3 × 5 × 11 = 48 × 5 × 11 = 240 × 11 = 2640So, the least common multiple of 66 and 240 is 2640.
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