Least Common Multiple (LCM) of 137 and 109
The least common multiple (LCM) of 137 and 109 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 137 and 109?
First, calculate the GCD of 137 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 109 = 1 remainder 28 |
| 2 | 109 ÷ 28 = 3 remainder 25 |
| 3 | 28 ÷ 25 = 1 remainder 3 |
| 4 | 25 ÷ 3 = 8 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 131 | 14541 |
| 40 and 105 | 840 |
| 153 and 135 | 2295 |
| 61 and 39 | 2379 |
| 94 and 159 | 14946 |