Least Common Multiple (LCM) of 48 and 129
The least common multiple (LCM) of 48 and 129 is 2064.
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 48 and 129?
First, calculate the GCD of 48 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 129 = 0 remainder 48 |
| 2 | 129 ÷ 48 = 2 remainder 33 |
| 3 | 48 ÷ 33 = 1 remainder 15 |
| 4 | 33 ÷ 15 = 2 remainder 3 |
| 5 | 15 ÷ 3 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 127 | 12954 |
| 84 and 44 | 924 |
| 128 and 77 | 9856 |
| 156 and 66 | 1716 |
| 54 and 31 | 1674 |