Least Common Multiple (LCM) of 108 and 69
The least common multiple (LCM) of 108 and 69 is 2484.
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 69?
First, calculate the GCD of 108 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 69 = 1 remainder 39 |
| 2 | 69 ÷ 39 = 1 remainder 30 |
| 3 | 39 ÷ 30 = 1 remainder 9 |
| 4 | 30 ÷ 9 = 3 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 196 and 34 | 3332 |
| 48 and 134 | 3216 |
| 124 and 117 | 14508 |
| 156 and 182 | 1092 |
| 87 and 61 | 5307 |