Solution

First of all, let us perform the prime factorization of 6, we get, So, we get, 6 = 2×3.....(i) Now, let us perform the prime factorization of 72, we get, So, we get, 72 = 2×2×2×3×3.....(ii) Now, let us perform the prime factorization of 120, we get, So, we get, 120 = 2×2×2×3×5......(iii) From equation (i), (ii) and (iii), we get, 6 = 2×3 72 = 2×2×2×3×3 120 = 2×2×2×3×5 From the above three equations, we can see that the common factors of 6, 72, and 120 is 2×3=6 So, we get the highest common factor or HCF of 6, 72, and 120 as 6. Now let us find the LCM of three numbers: 6, 72, and 120. We get, So, we get the LCM of 6, 72, and 120 as 2 × 2 × 2 × 3 × 3 × 5 = 360 Hence, the LCM of the three numbers is 360