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To start, we can factor each number into primes: 60 = 2 x 2 x 3 x 5 120 = 2 x 2 x 2 x 3 x 5 Then, we can identify the common and non-common prime factors of the two numbers. The common prime factors are 2, 3, and 5, and the non-common prime factors are 2 and 2. To find the LCM, we need to take the hRead more
To start, we can factor each number into primes:
60 = 2 x 2 x 3 x 5
120 = 2 x 2 x 2 x 3 x 5
Then, we can identify the common and non-common prime factors of the two numbers. The common prime factors are 2, 3, and 5, and the non-common prime factors are 2 and 2. To find the LCM, we need to take the highest power of each prime factor that appears in either factorization:
The highest power of 2 that appears is 2^3 = 8.
The highest power of 3 that appears is 3^1 = 3.
The highest power of 5 that appears is 5^1 = 5.
Multiplying these highest powers together, we get:
LCM(60, 120) = 2^3 x 3^1 x 5^1 = 120
Therefore, the LCM of 60 and 120 is 120.
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