Question

bridget has swimming lessons every fifth day and diving lessons every third day. If she had a swimming lesson and a diving lesson on May 5, when will be the next date on which she has both swimming and diving lessons?

Answer 1

she had both on May 5

swimming lessons every 5th day
5,10,15,20

diving lessons every 3rd day...
3,6,9,12,15

so they both have a common multiple of 15

so fifteen days after May 5 = May 20 <==

Answer 2

On May 20,

Explanation:

In order to calculate on which date both her lessons will fall on the same date, we take the LCM of 3 and 5.

Factors of 3 ⇒ 1 × 3

Factors of 5 ⇒ 1 × 5

Since 1 is common, we take it once and multiply with other non-common factors.

Therefore LCM = 1 × 3 × 5 = 15

Thus after 15 days of 5th may = 20th May

she has both lessons on May 20 after May 5.