Least Common Multiple (LCM) of 107 and 137
The least common multiple (LCM) of 107 and 137 is 14659.
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 107 and 137?
First, calculate the GCD of 107 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 137 = 0 remainder 107 |
| 2 | 137 ÷ 107 = 1 remainder 30 |
| 3 | 107 ÷ 30 = 3 remainder 17 |
| 4 | 30 ÷ 17 = 1 remainder 13 |
| 5 | 17 ÷ 13 = 1 remainder 4 |
| 6 | 13 ÷ 4 = 3 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 159 and 79 | 12561 |
| 117 and 30 | 1170 |
| 164 and 30 | 2460 |
| 65 and 36 | 2340 |
| 117 and 118 | 13806 |