Least Common Multiple (LCM) of 137 and 118
The least common multiple (LCM) of 137 and 118 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 137 and 118?
First, calculate the GCD of 137 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 118 = 1 remainder 19 |
| 2 | 118 ÷ 19 = 6 remainder 4 |
| 3 | 19 ÷ 4 = 4 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 53 and 119 | 6307 |
| 14 and 16 | 112 |
| 82 and 124 | 5084 |
| 89 and 103 | 9167 |
| 92 and 145 | 13340 |