1. **Problem:** Find the L.C.M. of 6, 72, and 120 using the prime factorisation method. 2. **Formula and Rules:** - The L.C.M. (Least Common Multiple) of numbers is found by taking the highest powers of all prime factors involved. - Prime factorisation means expressing each number as a product of prime numbers. 3. **Prime Factorisation:** - 6 = $2 \times 3$ - 72 = $2^3 \times 3^2$ - 120 = $2^3 \times 3 \times 5$ 4. **Find L.C.M.:** - Take the highest power of each prime factor: - For 2: highest power is $2^3$ - For 3: highest power is $3^2$ - For 5: highest power is $5^1$ 5. **Calculate L.C.M.:** $$\text{LCM} = 2^3 \times 3^2 \times 5 = 8 \times 9 \times 5$$ $$= 72 \times 5 = 360$$ 6. **Answer:** The L.C.M. of 6, 72, and 120 is **360**.