Least Common Multiple (LCM) of 117 and 60
The least common multiple (LCM) of 117 and 60 is 2340.
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 117 and 60?
First, calculate the GCD of 117 and 60 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 60 = 1 remainder 57 |
| 2 | 60 ÷ 57 = 1 remainder 3 |
| 3 | 57 ÷ 3 = 19 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 49 | 6321 |
| 53 and 78 | 4134 |
| 108 and 180 | 540 |
| 200 and 123 | 24600 |
| 23 and 45 | 1035 |