Least Common Multiple (LCM) of 108 and 137
The least common multiple (LCM) of 108 and 137 is 14796.
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 108 and 137?
First, calculate the GCD of 108 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 137 = 0 remainder 108 |
| 2 | 137 ÷ 108 = 1 remainder 29 |
| 3 | 108 ÷ 29 = 3 remainder 21 |
| 4 | 29 ÷ 21 = 1 remainder 8 |
| 5 | 21 ÷ 8 = 2 remainder 5 |
| 6 | 8 ÷ 5 = 1 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 97 | 14065 |
| 179 and 49 | 8771 |
| 153 and 80 | 12240 |
| 98 and 128 | 6272 |
| 75 and 99 | 2475 |