Question - Finding a Common Factor and Multiple

Given that the highest common factor (HCF) of 20 and p is 10, we have:

Factors of 20: 1, 2, 4, 5, 10, 20. The common factor with p must include 10.

To satisfy the HCF condition, p must include the factor 10. Therefore, p could be 10, 20, or another multiple of 10.

Given that the lowest common multiple (LCM) of 20 and p is 60, we calculate:

LCM(20, p) = (20 * p) / HCF(20, p)

Setting the equation for LCM:

(20 * p) / 10 = 60

20p = 600

p = 30

The smallest possible value of p is therefore:

p = 30