Question

If the sum of squares of two number is 164 and their hcf and lcm are 2 and 40 respectively then the numbers are

Answer 1

through this we show that there is no solution of this question

Answer 2

The numbers are 8 and 10

consider the numbers 8 and 10

sum of square of numbers are  8² + 10²

= 64 + 100

=164

8=23

If you want the LCM, you have to take the largest power of each prime factor:

10=2×5

8= 2 x 2 x 2

LCM=2³×5=40

HCF

To find the hcf, multiply all the prime factors common to both numbers:

Therefore, HCF = 2