Camryn practices the trumpet every 11^/text{th}11

th

11, start superscript, start text, t, h, end text, end superscript day and the flute every 3^/text{rd}3

rd

3, start superscript, start text, r, d, end text, end superscript day.

Camryn practiced both the trumpet and the flute today.

How many days until Camryn practices the trumpet and flute again in the same day?

33 days

in 33 days

Step-by-step explanation:

Trumpet practice is every 11 days. Flute practice is every 3 days.

You need the Least Common Multiple (the LCM) of the two numbers, 3 and 11.

Since 3 and 11 are prime, the LCM of 3 and 11 is their product.

LCM = 3 * 11 = 33

Answer: in 33 days

You can also solve this by listing multiples of 3 and 11 until you find the smallest number that is a multiple of both 3 and 11.

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, ...

Multiples of 11: 11, 22, 33, 44, ...

The smallest multiple of both 3 and 11 is the smallest number that shows in both lists. It is 33.