Which of the following statement(s) is/are correct? I. product of two positive numbers = Sum of their highest common factor and least common multiple II. Product of two positive numbers = Product of their highest common factor and least common multiple
Which of the following statement(s) is/are correct? I. product of two positive numbers = Sum of their highest common factor and least common multiple II. Product of two positive numbers = Product of their highest common factor and least common multiple Correct Answer Only II
Highest Common Factor is the product of the lowest powers of each of the prime factors that commonly occurs in both the numbers. For example:
12 = 2 × 2 × 3 = 22 × 31
18 = 2 × 3 × 3 = 21 × 32
Lowest Common Multiple is the product of the maximum number of each prime factor that occurs in either of the numbers. For example:
12 = 2 × 2 × 3 = 22 × 31
18 = 2 × 3 × 3 = 21 × 32
Hence, LCM of 12 and 18 is 22 × 32 = 36. Here, the lowest power of 2 and 3 is considered.
It should be noted: Product of two positive numbers = Product of their highest common factor and least common multiple. For example,
12 × 18 = 36 × 6 = 216.
Hence, we conclude that Product of two positive numbers = Product of their highest common factor and least common multiple.
