Least Common Multiple (LCM) of 101 and 137
The least common multiple (LCM) of 101 and 137 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 101 and 137?
First, calculate the GCD of 101 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 137 = 0 remainder 101 |
| 2 | 137 ÷ 101 = 1 remainder 36 |
| 3 | 101 ÷ 36 = 2 remainder 29 |
| 4 | 36 ÷ 29 = 1 remainder 7 |
| 5 | 29 ÷ 7 = 4 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 140 | 420 |
| 14 and 90 | 630 |
| 70 and 13 | 910 |
| 191 and 191 | 191 |
| 98 and 109 | 10682 |