The LCM of 6, 72 and 120 is:

1. Write each number as a product of primes: 6 = 2 x 3. 2. 72 = 2^3 x 3^2 and 120 = 2^3 x 3 x 5. 3. The LCM takes the highest power of every prime that appears: 2^3, 3^2 and 5. 4. So LCM = 8 x 9 x 5 = 360. 5. 180 misses a factor of 2 and 240 misses a factor of 3, so neither is a multiple of 72. _Source: syllabus Maths, Ch 1 'Real Numbers', S1.2 The Fundamental Theorem of Arithmetic_