Least Common Multiple (LCM) of 137 and 121
The least common multiple (LCM) of 137 and 121 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 137 and 121?
First, calculate the GCD of 137 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 121 = 1 remainder 16 |
| 2 | 121 ÷ 16 = 7 remainder 9 |
| 3 | 16 ÷ 9 = 1 remainder 7 |
| 4 | 9 ÷ 7 = 1 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 70 | 7630 |
| 190 and 81 | 15390 |
| 16 and 93 | 1488 |
| 113 and 199 | 22487 |
| 191 and 75 | 14325 |