Least Common Multiple (LCM) of 129 and 152
The least common multiple (LCM) of 129 and 152 is 19608.
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 152?
First, calculate the GCD of 129 and 152 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 152 = 0 remainder 129 |
| 2 | 152 ÷ 129 = 1 remainder 23 |
| 3 | 129 ÷ 23 = 5 remainder 14 |
| 4 | 23 ÷ 14 = 1 remainder 9 |
| 5 | 14 ÷ 9 = 1 remainder 5 |
| 6 | 9 ÷ 5 = 1 remainder 4 |
| 7 | 5 ÷ 4 = 1 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 108 | 7236 |
| 159 and 108 | 5724 |
| 145 and 112 | 16240 |
| 131 and 31 | 4061 |
| 35 and 190 | 1330 |