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To start, we can factor each number into primes: 120 = 2 x 2 x 2 x 3 x 5 90 = 2 x 3 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 2^2 and 3^2. To find the LCM, we need to take tRead more

To start, we can factor each number into primes:

120 = 2 x 2 x 2 x 3 x 5

90 = 2 x 3 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 2^2 and 3^2. 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 3^2 = 9.

The highest power of 5 that appears is 5^1 = 5.

Multiplying these highest powers together, we get:

LCM(120, 90) = 2^3 x 3^2 x 5^1 = 360

Therefore, the LCM of 120 and 90 is 360.

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