Least Common Multiple (LCM) of 137 and 116
The least common multiple (LCM) of 137 and 116 is 15892.
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 116?
First, calculate the GCD of 137 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 116 = 1 remainder 21 |
| 2 | 116 ÷ 21 = 5 remainder 11 |
| 3 | 21 ÷ 11 = 1 remainder 10 |
| 4 | 11 ÷ 10 = 1 remainder 1 |
| 5 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 193 and 53 | 10229 |
| 153 and 74 | 11322 |
| 90 and 147 | 4410 |
| 45 and 54 | 270 |
| 65 and 183 | 11895 |