Least Common Multiple (LCM) of 129 and 179
The least common multiple (LCM) of 129 and 179 is 23091.
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 129 and 179?
First, calculate the GCD of 129 and 179 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 179 = 0 remainder 129 |
| 2 | 179 ÷ 129 = 1 remainder 50 |
| 3 | 129 ÷ 50 = 2 remainder 29 |
| 4 | 50 ÷ 29 = 1 remainder 21 |
| 5 | 29 ÷ 21 = 1 remainder 8 |
| 6 | 21 ÷ 8 = 2 remainder 5 |
| 7 | 8 ÷ 5 = 1 remainder 3 |
| 8 | 5 ÷ 3 = 1 remainder 2 |
| 9 | 3 ÷ 2 = 1 remainder 1 |
| 10 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 40 | 3560 |
| 158 and 111 | 17538 |
| 186 and 41 | 7626 |
| 103 and 192 | 19776 |
| 145 and 120 | 3480 |