Least Common Multiple (LCM) of 117 and 184
The least common multiple (LCM) of 117 and 184 is 21528.
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 117 and 184?
First, calculate the GCD of 117 and 184 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 184 = 0 remainder 117 |
| 2 | 184 ÷ 117 = 1 remainder 67 |
| 3 | 117 ÷ 67 = 1 remainder 50 |
| 4 | 67 ÷ 50 = 1 remainder 17 |
| 5 | 50 ÷ 17 = 2 remainder 16 |
| 6 | 17 ÷ 16 = 1 remainder 1 |
| 7 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 69 | 69 |
| 10 and 18 | 90 |
| 45 and 116 | 5220 |
| 141 and 35 | 4935 |
| 113 and 18 | 2034 |