Least Common Multiple (LCM) of 117 and 167
The least common multiple (LCM) of 117 and 167 is 19539.
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 167?
First, calculate the GCD of 117 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 167 = 0 remainder 117 |
| 2 | 167 ÷ 117 = 1 remainder 50 |
| 3 | 117 ÷ 50 = 2 remainder 17 |
| 4 | 50 ÷ 17 = 2 remainder 16 |
| 5 | 17 ÷ 16 = 1 remainder 1 |
| 6 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 137 | 4384 |
| 189 and 100 | 18900 |
| 199 and 35 | 6965 |
| 104 and 32 | 416 |
| 30 and 21 | 210 |