Least Common Multiple (LCM) of 61 and 137
The least common multiple (LCM) of 61 and 137 is 8357.
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 61 and 137?
First, calculate the GCD of 61 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 61 ÷ 137 = 0 remainder 61 |
| 2 | 137 ÷ 61 = 2 remainder 15 |
| 3 | 61 ÷ 15 = 4 remainder 1 |
| 4 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 124 and 195 | 24180 |
| 105 and 14 | 210 |
| 158 and 179 | 28282 |
| 182 and 113 | 20566 |
| 100 and 89 | 8900 |