Least Common Multiple (LCM) of 117 and 166
The least common multiple (LCM) of 117 and 166 is 19422.
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 166?
First, calculate the GCD of 117 and 166 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 166 = 0 remainder 117 |
| 2 | 166 ÷ 117 = 1 remainder 49 |
| 3 | 117 ÷ 49 = 2 remainder 19 |
| 4 | 49 ÷ 19 = 2 remainder 11 |
| 5 | 19 ÷ 11 = 1 remainder 8 |
| 6 | 11 ÷ 8 = 1 remainder 3 |
| 7 | 8 ÷ 3 = 2 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 91 and 139 | 12649 |
| 30 and 54 | 270 |
| 145 and 88 | 12760 |
| 45 and 31 | 1395 |
| 129 and 158 | 20382 |