Question

find LCM and HCF of 400 and 625 and prove that the product of HCF LCM equals to product of numbers​

Answer 1

Answer:

LCM stands for Lowest Common Multiple and HCF stands for Highest Common Factor.

Given numbers -

400 and 625

For LCM,

Split the numbers into their prime factors.

400 = 2 * 2 * 2 * 2 * 5 * 5

625 = 5 * 5 * 5 * 5

Now, write the factors in the form of table as shown in the first attachment.

Then, the product of largest factors will be the LCM.

LCM = 2⁴ * 5⁴ = 10000

For HCF,

Split the numbers into their respective factors.

400 = 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400

625 = 1, 5, 25, 125, 625

Now, we see that the highest/greatest common factor is 25.

Hence, HCF = 25

For proof,

Product of numbers = 400 * 625 = 250000

Product of HCF and LCM = 25 * 10000 = 250000

Since, Product of numbers = Product of HCF and LCM

$\boxed{\boxed{Proved}}$