Least Common Multiple (LCM) of 129 and 156
The least common multiple (LCM) of 129 and 156 is 6708.
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 156?
First, calculate the GCD of 129 and 156 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 156 = 0 remainder 129 |
| 2 | 156 ÷ 129 = 1 remainder 27 |
| 3 | 129 ÷ 27 = 4 remainder 21 |
| 4 | 27 ÷ 21 = 1 remainder 6 |
| 5 | 21 ÷ 6 = 3 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 144 | 12816 |
| 21 and 78 | 546 |
| 118 and 79 | 9322 |
| 170 and 166 | 14110 |
| 178 and 171 | 30438 |