Least Common Multiple (LCM) of 117 and 137
The least common multiple (LCM) of 117 and 137 is 16029.
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 137?
First, calculate the GCD of 117 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 137 = 0 remainder 117 |
| 2 | 137 ÷ 117 = 1 remainder 20 |
| 3 | 117 ÷ 20 = 5 remainder 17 |
| 4 | 20 ÷ 17 = 1 remainder 3 |
| 5 | 17 ÷ 3 = 5 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 170 and 70 | 1190 |
| 54 and 54 | 54 |
| 195 and 160 | 6240 |
| 35 and 29 | 1015 |
| 40 and 35 | 280 |