Find the product of HCF and LCM of 510 and 92.

To find the product of the Highest Common Factor (HCF) and the Least Common Multiple (LCM) of the numbers 510 and 92, we can follow a systematic approach.

Step 1: Calculate the HCF

The HCF of two numbers is the largest number that divides both of them without leaving a remainder. For 510 and 92, we can use the prime factorization method:

• Prime factorization of 510: 2 × 3 × 5 × 17
• Prime factorization of 92: 2 × 2 × 23

The common factor here is 2. Therefore, the HCF is:

HCF = 2

Step 2: Calculate the LCM

The LCM is the smallest number that both 510 and 92 can divide into without a remainder. We can find it using the formula:

LCM = (Product of the numbers) / HCF

Calculating the product of 510 and 92:

Product = 510 × 92 = 46,920

Now, using the HCF we found:

LCM = 46,920 / 2 = 23,460

Step 3: Find the Product of HCF and LCM

Now, we can find the product of the HCF and LCM:

Product of HCF and LCM = HCF × LCM = 2 × 23,460 = 46,920

Final Result

The product of the HCF and LCM of 510 and 92 is:

46,920