Least Common Multiple (LCM) of 114 and 60
The least common multiple (LCM) of 114 and 60 is 1140.
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 114 and 60?
First, calculate the GCD of 114 and 60 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 60 = 1 remainder 54 |
| 2 | 60 ÷ 54 = 1 remainder 6 |
| 3 | 54 ÷ 6 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 164 and 150 | 12300 |
| 13 and 57 | 741 |
| 155 and 19 | 2945 |
| 35 and 127 | 4445 |
| 197 and 31 | 6107 |