Question

Find HCF and LCM of 510 and 92 by applying the prime factorization method.

Answer 1

Hint: Break 92 and 510 in prime factors. Then take the lowest power of each of the prime factors to compute HCF. Similarly, to find LCM take the highest power of each of the prime factors.

Complete step-by-step answer:
Given 510 and 92,
92 can be factorized as \[2 \times 2 \times 23\].
510 can be factorized as \[2 \times 3 \times 5 \times 17\].
After prime factoring the numbers given, let us list down all the prime factors.
Then take the lowest/least power of each of the prime factors. This is the method to compute HCF. The lowest power of the prime factor 2 is 1, which is to say we have a 2 in both the numbers.
Hence HCF is 2.
Next, take the highest power of each of the prime factors. This is the method to compute LCM. The highest power of the prime factors 2, 3, 5, 17 and 23 are 2, 1, 1, 1 and 1 respectively.
Therefore LCM is \[{2^2} \times 3 \times 5 \times 17 \times 23 = 23460\]

Hence the HCF and LCM of 510 and 92 are 2 and 23460 respectively.

Note: LCM of 92 and 510 , is the smallest number divisible by 92 and 510 both. Therefore we have to take maximum power of all factors to calculate LCM.
Whereas HCF of 92 and 510 is the greatest number that divides both 92 and 510.
For 2 numbers always the product of LCM and HCF is equal to the Product of the given two numbers.