Least Common Multiple (LCM) of 91 and 129
The least common multiple (LCM) of 91 and 129 is 11739.
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 91 and 129?
First, calculate the GCD of 91 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 91 ÷ 129 = 0 remainder 91 |
| 2 | 129 ÷ 91 = 1 remainder 38 |
| 3 | 91 ÷ 38 = 2 remainder 15 |
| 4 | 38 ÷ 15 = 2 remainder 8 |
| 5 | 15 ÷ 8 = 1 remainder 7 |
| 6 | 8 ÷ 7 = 1 remainder 1 |
| 7 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 176 | 1232 |
| 160 and 129 | 20640 |
| 27 and 84 | 756 |
| 86 and 47 | 4042 |
| 14 and 16 | 112 |