Least Common Multiple (LCM) of 117 and 183
The least common multiple (LCM) of 117 and 183 is 7137.
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 183?
First, calculate the GCD of 117 and 183 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 183 = 0 remainder 117 |
| 2 | 183 ÷ 117 = 1 remainder 66 |
| 3 | 117 ÷ 66 = 1 remainder 51 |
| 4 | 66 ÷ 51 = 1 remainder 15 |
| 5 | 51 ÷ 15 = 3 remainder 6 |
| 6 | 15 ÷ 6 = 2 remainder 3 |
| 7 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 63 | 945 |
| 200 and 112 | 2800 |
| 151 and 108 | 16308 |
| 105 and 23 | 2415 |
| 139 and 130 | 18070 |