Kevin, Yone, and Miroki work part-time at the YMCA in Kamloops. Kevin works every second day. Yone works every third day. Miroki works every fourth day. Today, they worked together. When will they work together again?
kevin works on days # 1,3,5,7,9,11,13,15,....
yone works on days # 1,4,7,10,13,16....
miroko works days 1, 5, 9, 13, .....
To find out when Kevin, Yone, and Miroki will work together again, we need to determine the least common multiple (LCM) of their workdays.
Kevin works every second day, so his workdays follow the pattern: 2, 4, 6, 8, 10, ...
Yone works every third day, so his workdays follow the pattern: 3, 6, 9, 12, 15, ...
Miroki works every fourth day, so his workdays follow the pattern: 4, 8, 12, 16, 20, ...
To find the LCM, we look for the smallest number that is divisible by 2, 3, and 4. Start by listing out the multiples of each number:
Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, ...
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, ...
Multiples of 4: 4, 8, 12, 16, 20, 24, ...
By examining the lists, we can see that 12 is the smallest number that is divisible by 2, 3, and 4. Therefore, Kevin, Yone, and Miroki will work together again on the 12th day.
Please note that if you encounter more than 3 individuals with different work patterns, you would need to find the LCM of their workdays using the same approach.
LCM(2,3,4) = 12
Kevin, 2 = 2, 4, 6, 8 , 10, 12, 14.
Yone, 3 = 3, 6, 9, 12, 15, 18, 21.
Miroki, 4 = 4, 8, 12, 16, 20, 24, 27.
They work together on the 12th day.