Least Common Multiple (LCM) of 108 and 29
The least common multiple (LCM) of 108 and 29 is 3132.
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 108 and 29?
First, calculate the GCD of 108 and 29 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 29 = 3 remainder 21 |
| 2 | 29 ÷ 21 = 1 remainder 8 |
| 3 | 21 ÷ 8 = 2 remainder 5 |
| 4 | 8 ÷ 5 = 1 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 52 | 6188 |
| 53 and 177 | 9381 |
| 144 and 79 | 11376 |
| 108 and 12 | 108 |
| 178 and 50 | 4450 |