Least Common Multiple (LCM) of 117 and 181
The least common multiple (LCM) of 117 and 181 is 21177.
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 181?
First, calculate the GCD of 117 and 181 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 181 = 0 remainder 117 |
| 2 | 181 ÷ 117 = 1 remainder 64 |
| 3 | 117 ÷ 64 = 1 remainder 53 |
| 4 | 64 ÷ 53 = 1 remainder 11 |
| 5 | 53 ÷ 11 = 4 remainder 9 |
| 6 | 11 ÷ 9 = 1 remainder 2 |
| 7 | 9 ÷ 2 = 4 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 153 | 1224 |
| 182 and 198 | 18018 |
| 153 and 133 | 20349 |
| 90 and 116 | 5220 |
| 93 and 152 | 14136 |