Question

Find the list number which when divided by 60 ,120and 180 leaves a remainder 5 in each case .

Answer 1

Given:

• When 60,120 and 180 is divided by a least number.
• It leaves 5 as a remainder.

To Find:

• Find the least number = ?

Solution:

Take the LCM of 60,120 and 180

$\sf \: 60 = 2 \times 2 \times 3 \times 5 \\ \\ \sf \: 120 = 2 \times 2 \times 2 \times 3 \times 5 \\ \\ \sf \: 180 = 2 \times 2 \times 3 \times 3 \times 5$

$\sf \: lcm = 2 \times 2 \times 3 \times 5 \times 3 \times 2 \\ \sf \: = 360$

Now,

• We are given that the remainder 5 in each case. So, now we will add 5 to the LCM.

$\sf \: least \: no. = 360 + 5 = 365$