Least Common Multiple (LCM) of 137 and 101
The least common multiple (LCM) of 137 and 101 is 13837.
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 101?
First, calculate the GCD of 137 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 101 = 1 remainder 36 |
| 2 | 101 ÷ 36 = 2 remainder 29 |
| 3 | 36 ÷ 29 = 1 remainder 7 |
| 4 | 29 ÷ 7 = 4 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 177 and 195 | 11505 |
| 121 and 72 | 8712 |
| 103 and 83 | 8549 |
| 166 and 31 | 5146 |
| 148 and 196 | 7252 |