Least Common Multiple (LCM) of 137 and 117
The least common multiple (LCM) of 137 and 117 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 137 and 117?
First, calculate the GCD of 137 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 117 = 1 remainder 20 |
| 2 | 117 ÷ 20 = 5 remainder 17 |
| 3 | 20 ÷ 17 = 1 remainder 3 |
| 4 | 17 ÷ 3 = 5 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 141 and 31 | 4371 |
| 157 and 141 | 22137 |
| 45 and 13 | 585 |
| 46 and 79 | 3634 |
| 113 and 50 | 5650 |