Least Common Multiple (LCM) of 137 and 18
The least common multiple (LCM) of 137 and 18 is 2466.
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 18?
First, calculate the GCD of 137 and 18 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 18 = 7 remainder 11 |
| 2 | 18 ÷ 11 = 1 remainder 7 |
| 3 | 11 ÷ 7 = 1 remainder 4 |
| 4 | 7 ÷ 4 = 1 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 71 | 9727 |
| 187 and 77 | 1309 |
| 18 and 60 | 180 |
| 183 and 78 | 4758 |
| 104 and 42 | 2184 |