To find the Least Common Multiple (LCM) of 45, 75, and 90, we first need to find the prime factorization of each number.
45 = 3 x 3 x 5 75 = 3 x 5 x 5 90 = 2 x 3 x 3 x 5
Next, we identify the highest power of each prime factor that appears in any of the factorizations. The LCM is then calculated by multiplying these highest powers together.
Therefore, the LCM of 45, 75, and 90 is 2 x 3^2 x 5^2 = 450.
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The GCM is infinite.
The GCF is 15.
The LCM is 450.
Check it.
75 x 90 = 6750
450 x 15 = 6750
It checks.