Given :5³×3⁴ and 5²×3¹×2¹
Determine the following
HCF
LCM
To determine the HCF (Highest Common Factor), we need to find the highest power of common factors in both expressions.
5³ × 3⁴:
The prime factors in this expression are 5 and 3.
The highest power of 5 is 5³ (since 5 is raised to the power of 3).
The highest power of 3 is 3⁴ (since 3 is raised to the power of 4).
5² × 3¹ × 2¹:
The prime factors in this expression are 5, 3, and 2.
The highest power of 5 is 5².
The highest power of 3 is 3¹.
The highest power of 2 is 2¹.
HCF:
To find the HCF, we take the highest power of common factors, which are:
5² × 3¹.
Therefore, the HCF is 5² × 3¹.
To determine the LCM (Lowest Common Multiple), we need to find the product of the highest powers of all the prime factors in both expressions.
5³ × 3⁴:
The prime factors in this expression are 5 and 3.
The highest power of 5 is 5³.
The highest power of 3 is 3⁴.
5² × 3¹ × 2¹:
The prime factors in this expression are 5, 3, and 2.
The highest power of 5 is 5².
The highest power of 3 is 3¹.
The highest power of 2 is 2¹.
LCM:
To find the LCM, we take the product of the highest powers of all the prime factors, which are:
5³ × 3⁴ × 2¹.
Therefore, the LCM is 5³ × 3⁴ × 2¹.