Least Common Multiple (LCM) of 60 and 117
The least common multiple (LCM) of 60 and 117 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 60 and 117?
First, calculate the GCD of 60 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 60 ÷ 117 = 0 remainder 60 |
| 2 | 117 ÷ 60 = 1 remainder 57 |
| 3 | 60 ÷ 57 = 1 remainder 3 |
| 4 | 57 ÷ 3 = 19 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 146 | 146 |
| 53 and 27 | 1431 |
| 52 and 112 | 1456 |
| 165 and 168 | 9240 |
| 106 and 130 | 6890 |