The farmer and daughter working together would take 6 days to plant the field
<h3><u>Solution:</u></h3>
Time taken by farmer to plant a field is 10 days
Time taken by his daughter to plant a field is 15 days
<em><u>Now lets find L.C.M of 10 and 15</u></em>
List all prime factors for each number.
Prime factorization of 10 = 2 x 5
Prime factorization of 15 = 3 x 5
For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.
The new superset list is
2, 3, 5
Multiply these factors together to find the LCM.
LCM = 2 x 3 x 5 = 30
Thus L.C.M of 10 and 15 is 30
![\begin{array}{l}{\text { Efficiency of farmer }=\frac{\text { Total Work }}{\text { Time Taken }}} \\\\ {\text { Efficiency of farmer }=\frac{30}{10}=3} \\\\ {\text { Efficiency of her daughter }=\frac{\text { Total Work }}{\text { Time Taken }}} \\\\ {\text { Efficiency of daughter }=\frac{30}{15}=2}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7B%5Ctext%20%7B%20Efficiency%20of%20farmer%20%7D%3D%5Cfrac%7B%5Ctext%20%7B%20Total%20Work%20%7D%7D%7B%5Ctext%20%7B%20Time%20Taken%20%7D%7D%7D%20%5C%5C%5C%5C%20%7B%5Ctext%20%7B%20Efficiency%20of%20farmer%20%7D%3D%5Cfrac%7B30%7D%7B10%7D%3D3%7D%20%5C%5C%5C%5C%20%7B%5Ctext%20%7B%20Efficiency%20of%20her%20daughter%20%7D%3D%5Cfrac%7B%5Ctext%20%7B%20Total%20Work%20%7D%7D%7B%5Ctext%20%7B%20Time%20Taken%20%7D%7D%7D%20%5C%5C%5C%5C%20%7B%5Ctext%20%7B%20Efficiency%20of%20daughter%20%7D%3D%5Cfrac%7B30%7D%7B15%7D%3D2%7D%5Cend%7Barray%7D)
<em><u>When both of them work together:</u></em>
![\text { Time taken }=\frac{\text { Total work }}{\text { Total Efficiency }}=\frac{30}{3+2}=\frac{30}{5}=6 \text { days }](https://tex.z-dn.net/?f=%5Ctext%20%7B%20Time%20taken%20%7D%3D%5Cfrac%7B%5Ctext%20%7B%20Total%20work%20%7D%7D%7B%5Ctext%20%7B%20Total%20Efficiency%20%7D%7D%3D%5Cfrac%7B30%7D%7B3%2B2%7D%3D%5Cfrac%7B30%7D%7B5%7D%3D6%20%5Ctext%20%7B%20days%20%7D)
Hence, both of them can complete the work in 6 days