Least Common Multiple (LCM) of 108 and 61
The least common multiple (LCM) of 108 and 61 is 6588.
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 61?
First, calculate the GCD of 108 and 61 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 61 = 1 remainder 47 |
| 2 | 61 ÷ 47 = 1 remainder 14 |
| 3 | 47 ÷ 14 = 3 remainder 5 |
| 4 | 14 ÷ 5 = 2 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 74 and 16 | 592 |
| 119 and 115 | 13685 |
| 68 and 121 | 8228 |
| 47 and 91 | 4277 |
| 83 and 165 | 13695 |