Least Common Multiple (LCM) of 13 and 127
The least common multiple (LCM) of 13 and 127 is 1651.
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 13 and 127?
First, calculate the GCD of 13 and 127 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 13 ÷ 127 = 0 remainder 13 |
| 2 | 127 ÷ 13 = 9 remainder 10 |
| 3 | 13 ÷ 10 = 1 remainder 3 |
| 4 | 10 ÷ 3 = 3 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 137 | 19865 |
| 29 and 63 | 1827 |
| 90 and 191 | 17190 |
| 114 and 190 | 570 |
| 190 and 116 | 11020 |