Verification of the Product of Numbers with HCF and LCM

Pair of Numbers: 24 and 54

To verify if the product of the given numbers is equal to the product of their HCF and LCM, we need to follow the steps given below:

Step 1: Find the HCF of the given numbers.

To find the HCF of 24 and 54, we can use the following methods:

- Prime factorization method: The prime factors of 24 are 2 x 2 x 2 x 3. The prime factors of 54 are 2 x 3 x 3 x 3. The common factors are 2 and 3. Therefore, the HCF of 24 and 54 is 2 x 3 = 6.

- Division method: We can use the division method to find the HCF of the given numbers. We divide the larger number by the smaller number and find the remainder. Then we divide the smaller number by the remainder and find the new remainder. We continue this process until the remainder becomes zero. The last divisor is the HCF of the given numbers. Using this method, we get the HCF of 24 and 54 as 6.

Step 2: Find the LCM of the given numbers.

To find the LCM of 24 and 54, we can use the following methods:

- Prime factorization method: The prime factors of 24 are 2 x 2 x 2 x 3. The prime factors of 54 are 2 x 3 x 3 x 3. The LCM is the product of all the prime factors with the highest power. Therefore, the LCM of 24 and 54 is 2 x 2 x 2 x 3 x 3 x 3 = 216.

- Division method: We can use the division method to find the LCM of the given numbers. We divide the larger number by the HCF and multiply it by the smaller number. The result is the LCM of the given numbers. Using this method, we get the LCM of 24 and 54 as (54/6) x 24 = 216.

Step 3: Verify the product of the numbers with the product of their HCF and LCM.

The product of 24 and 54 is 24 x 54 = 1296.

The product of their HCF and LCM is 6 x 216 = 1296.

Therefore, the product of the given numbers is equal to the product of their HCF and LCM.

Conclusion: Hence, we have verified that the product of 24 and 54 is equal to the product of their HCF and LCM.

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