Least Common Multiple (LCM) of 61 and 108
The least common multiple (LCM) of 61 and 108 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 61 and 108?
First, calculate the GCD of 61 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 61 ÷ 108 = 0 remainder 61 |
| 2 | 108 ÷ 61 = 1 remainder 47 |
| 3 | 61 ÷ 47 = 1 remainder 14 |
| 4 | 47 ÷ 14 = 3 remainder 5 |
| 5 | 14 ÷ 5 = 2 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 124 and 58 | 3596 |
| 181 and 174 | 31494 |
| 52 and 136 | 1768 |
| 116 and 104 | 3016 |
| 179 and 75 | 13425 |