Least Common Multiple (LCM) of 121 and 137
The least common multiple (LCM) of 121 and 137 is 16577.
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 121 and 137?
First, calculate the GCD of 121 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 121 ÷ 137 = 0 remainder 121 |
| 2 | 137 ÷ 121 = 1 remainder 16 |
| 3 | 121 ÷ 16 = 7 remainder 9 |
| 4 | 16 ÷ 9 = 1 remainder 7 |
| 5 | 9 ÷ 7 = 1 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 90 | 990 |
| 82 and 129 | 10578 |
| 39 and 103 | 4017 |
| 103 and 169 | 17407 |
| 20 and 25 | 100 |