Question

Using fundamental theorem o f Arithmetic , find the LCM and HCF 816 and 170

Answer 1

your answer hope it will help

Answer 2

Explanation:

"HCF of two or more numbers = Product of the smallest power of each common prime factor involved in the numbers.

LCM of two or more numbers = Product of the greatest power of each prime factor involved in the numbers with highest power.

Prime factorisation of 816 and 170 is:

816=2x2x2x2x3x17

=2^4x3^1x17^1

170=2x5x17

=2^1x5^1x17^1

By using fundamental theorem of arithmetic:

LCM(816,170)=2^4x3^1x5^1x17^1

=16x3x5x17

=48x5x17

=240x17

=4080

LCM=4080

HCF(816,170)=2^1x17^1

=34

Hence the LCM and HCF are 4080 and 34"