Least Common Multiple (LCM) of 129 and 168
The least common multiple (LCM) of 129 and 168 is 7224.
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 168?
First, calculate the GCD of 129 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 168 = 0 remainder 129 |
| 2 | 168 ÷ 129 = 1 remainder 39 |
| 3 | 129 ÷ 39 = 3 remainder 12 |
| 4 | 39 ÷ 12 = 3 remainder 3 |
| 5 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 150 | 1050 |
| 30 and 49 | 1470 |
| 101 and 127 | 12827 |
| 78 and 109 | 8502 |
| 184 and 134 | 12328 |