Find the LCM of 50 and 75.
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To find the LCM (Least Common Multiple) of 50 and 75, we can use the prime factorization method:
Prime factorization of 50: 50 = 2 × 5 × 5 Prime factorization of 75: 75 = 3 × 5 × 5
The LCM is the smallest number that is divisible by both 50 and 75. To find the LCM, we need to find the highest power of each prime factor that appears in either factorization, and then multiply those powers together.
In this case, the prime factors are 2, 3, 5. The highest power of 2 that appears is 1 (from the factorization of 50), the highest power of 3 that appears is 1 (from the factorization of 75), and the highest power of 5 that appears is 2 (from both factorizations). Therefore, the LCM of 50 and 75 is:
LCM(50, 75) = 2^1 × 3^1 × 5^2 = 150