Least Common Multiple (LCM) of 101 and 184
The least common multiple (LCM) of 101 and 184 is 18584.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 101 and 184?
First, calculate the GCD of 101 and 184 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 184 = 0 remainder 101 |
| 2 | 184 ÷ 101 = 1 remainder 83 |
| 3 | 101 ÷ 83 = 1 remainder 18 |
| 4 | 83 ÷ 18 = 4 remainder 11 |
| 5 | 18 ÷ 11 = 1 remainder 7 |
| 6 | 11 ÷ 7 = 1 remainder 4 |
| 7 | 7 ÷ 4 = 1 remainder 3 |
| 8 | 4 ÷ 3 = 1 remainder 1 |
| 9 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 19 and 93 | 1767 |
| 167 and 155 | 25885 |
| 144 and 180 | 720 |
| 85 and 13 | 1105 |
| 103 and 45 | 4635 |