three varieties of flowers bloom every 24, 48, and 52 days. suppose today the three are flowering, after how many days will they bloom together?
24 = 2^2 * 3
48 = 2^3 * 3
52 = 2^2 * 13
so, what is the LCM?
To find out when all three varieties of flowers will bloom together, we need to find the lowest common multiple (LCM) of the three blooming periods.
The blooming periods are:
1) Variety 1: 24 days
2) Variety 2: 48 days
3) Variety 3: 52 days
To find the LCM, we can break down each blooming period into its prime factors:
1) Variety 1: 24 = 2^3 * 3
2) Variety 2: 48 = 2^4 * 3
3) Variety 3: 52 = 2^2 * 13
Now, take the highest power of each prime factor:
- The highest power of 2 is 2^4 = 16.
- The highest power of 3 is 3.
- The highest power of 13 is 13.
Multiply these highest powers together to find the LCM:
LCM = 2^4 * 3 * 13
= 208 * 3
= 624
Therefore, the three varieties of flowers will bloom together after 624 days.
To find out when the three varieties of flowers will bloom together, we need to find the least common multiple (LCM) of their blooming periods. The LCM is the smallest number that is divisible by all the given numbers.
In this case, we have the blooming periods of 24, 48, and 52 days.
Step 1: Prime factorize each number:
24 = 2^3 * 3^1
48 = 2^4 * 3^1
52 = 2^2 * 13^1
Step 2: Identify the highest power of each prime factor:
2: 4
3: 1
13: 1
Step 3: Calculate the LCM by multiplying each prime factor raised to its highest power:
LCM = 2^4 * 3^1 * 13^1
= 384
Therefore, the three varieties of flowers will bloom together after 384 days.