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 |
|---|---|
| 110 and 180 | 1980 |
| 157 and 124 | 19468 |
| 195 and 90 | 1170 |
| 63 and 94 | 5922 |
| 149 and 199 | 29651 |