Find the HCF of 300 and 450 and hence find their LCM
Answers
Answer:
gcf, hcf, gcd (300; 450) = 150 = 2 × 3 × 5^2: greatest (highest) common factor (divisor), calculated. The numbers have common prime factors.
Step-by-step explanation:
If "t" is a factor (divisor) of "a" then among the prime factors of the prime factorization of "t" will appear only prime factors that also appear in the prime factorization of "a", and the maximum of their exponents is at most equal to those involved in the prime factorization of "a".
For example, 12 is a divisor of 60:
12 = 2 × 2 × 3 = 22 × 3
60 = 2 × 2 × 3 × 5 = 22 × 3 × 5
If "t" is a common factor of "a" and "b", then the prime factorization of "t" contains only prime factors involved in the prime factorizations of both "a" and "b", by the lower powers (exponents).
For example, 12 is the common factor of 48 and 360.
12 = 22 × 3
48 = 24 × 3
360 = 23 × 32 × 5
Please note that 48 and 360 have more factors (divisors): 2, 3, 4, 6, 8, 12, 24. Among them, 24 is the greatest common factor, GCF (or the greatest common divisor, GCD, or the highest common factor, HCF) of 48 and 360.
Answer:
HCF of 300 and 450 is 2×3×5×5