What are the Highest Common Factor and Lowest Common Multiple of 6, 72, 120?

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