Least Common Multiple (LCM) of 60 and 109
The least common multiple (LCM) of 60 and 109 is 6540.
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 60 and 109?
First, calculate the GCD of 60 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 60 ÷ 109 = 0 remainder 60 |
| 2 | 109 ÷ 60 = 1 remainder 49 |
| 3 | 60 ÷ 49 = 1 remainder 11 |
| 4 | 49 ÷ 11 = 4 remainder 5 |
| 5 | 11 ÷ 5 = 2 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 154 and 96 | 7392 |
| 28 and 67 | 1876 |
| 191 and 90 | 17190 |
| 33 and 31 | 1023 |
| 195 and 71 | 13845 |