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To find the least common multiple (LCM) of 35, 40, and 120, we first need to find the prime factorization of each number.
35 = 5 x 7 40 = 2^3 x 5 120 = 2^3 x 3 x 5
Next, we identify the highest power of each prime factor that appears in any of the numbers: 2^3, 3, 5, and 7.
Multiplying these together gives us the LCM: 2^3 x 3 x 5 x 7 = 840. Therefore, the least common multiple of 35, 40, and 120 is 840.
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