Least Common Multiple (LCM) of 109 and 137
The least common multiple (LCM) of 109 and 137 is 14933.
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 109 and 137?
First, calculate the GCD of 109 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 137 = 0 remainder 109 |
| 2 | 137 ÷ 109 = 1 remainder 28 |
| 3 | 109 ÷ 28 = 3 remainder 25 |
| 4 | 28 ÷ 25 = 1 remainder 3 |
| 5 | 25 ÷ 3 = 8 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 94 | 6580 |
| 77 and 96 | 7392 |
| 182 and 169 | 2366 |
| 123 and 134 | 16482 |
| 74 and 96 | 3552 |