Least Common Multiple (LCM) of 109 and 60
The least common multiple (LCM) of 109 and 60 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 109 and 60?
First, calculate the GCD of 109 and 60 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 60 = 1 remainder 49 |
| 2 | 60 ÷ 49 = 1 remainder 11 |
| 3 | 49 ÷ 11 = 4 remainder 5 |
| 4 | 11 ÷ 5 = 2 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 64 and 174 | 5568 |
| 11 and 144 | 1584 |
| 120 and 144 | 720 |
| 45 and 118 | 5310 |
| 38 and 95 | 190 |