Question

Find the HCF and LCM of 75 and 120 by prime factorization

Answer 1

Step-by-step explanation:

75 = 3 × 5 × 5

Find the prime factorization of 120

120 = 2 × 2 × 2 × 3 × 5

Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the LCM:

LCM = 2 × 2 × 2 × 3 × 5 × 5

LCM = 600

Find the prime factorization of 75

75 = 3 × 5 × 5

Find the prime factorization of 120

120 = 2 × 2 × 2 × 3 × 5

To find the HCF, multiply all the prime factors common to both numbers:

Therefore, HCF = 3 × 5

HCF = 15

Answer 2

Step-by-step explanation:

75= 3×5×5

120=2×2×2×3×5

LCM=2×2×2×3×5×5=600

HCF=3×5=15