Least Common Multiple (LCM) of 118 and 137
The least common multiple (LCM) of 118 and 137 is 16166.
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 118 and 137?
First, calculate the GCD of 118 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 118 ÷ 137 = 0 remainder 118 |
| 2 | 137 ÷ 118 = 1 remainder 19 |
| 3 | 118 ÷ 19 = 6 remainder 4 |
| 4 | 19 ÷ 4 = 4 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 41 and 40 | 1640 |
| 102 and 190 | 9690 |
| 136 and 97 | 13192 |
| 191 and 192 | 36672 |
| 23 and 173 | 3979 |