Least Common Multiple (LCM) of 69 and 108
The least common multiple (LCM) of 69 and 108 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 69 and 108?
First, calculate the GCD of 69 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 108 = 0 remainder 69 |
| 2 | 108 ÷ 69 = 1 remainder 39 |
| 3 | 69 ÷ 39 = 1 remainder 30 |
| 4 | 39 ÷ 30 = 1 remainder 9 |
| 5 | 30 ÷ 9 = 3 remainder 3 |
| 6 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 124 | 3348 |
| 134 and 199 | 26666 |
| 53 and 120 | 6360 |
| 66 and 190 | 6270 |
| 196 and 195 | 38220 |