Number and theory test

Question

Patsy has cheerleading practice every fourth day. She wants to be in the school play, but they have practice every sixth day. If both start on September 5th, what would be the next date she has to choose between cheerleading and play practice? Show your work and explain.

It is okay if you don't answer, I just want to understand this topic

I'm in 6th grade elearning academy

Answer 1

Sept 5

same day, Sept 5

Sept 4+5= 9 and Sept 5+6 = 11, different days

cheerleading school play

add 4 and 6 again

Sept 9 + 4 = 13, Sept 11 + 6 = Sept 17, different days

cheer leading school play

0, 4, 8, 12, 16, 20, 24

0, 6, 12, 18, 24

are two arithmetic sequences which coincide at 0 and 12

0 is Sept. 5

12 is Sept 5+12 = Sept 17

they coincide every 12 days

4 = 2x2

6 =3x2

take each integer fact of 4 and 6 and multiply them together, but not using any integer more times than the maximum time it appear as a factor in either 4 or 6

2x2x3 = 12

add 4

Sept 13 +4 = Sept. 17 which is the same day at in the 6 days cycle

SEPT 17 is the next day she has to choose

It's called the LCM, least common multiple or lowest common multiple or smallest common multiple.

It's the number that is evenly divisible by both numbers, with no remainder. 12 is divisible by 4 and by 6, There is no smaller number divisible by both 4 and 6, so 12 is the LCM

every 12 days the 4 cycle and 6 cycle of days coincide.

24 and 36 common multiples of 4 and 6, but not a LCM