Least Common Multiple (LCM) of 117 and 50
The least common multiple (LCM) of 117 and 50 is 5850.
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 50?
First, calculate the GCD of 117 and 50 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 50 = 2 remainder 17 |
| 2 | 50 ÷ 17 = 2 remainder 16 |
| 3 | 17 ÷ 16 = 1 remainder 1 |
| 4 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 70 | 1120 |
| 168 and 61 | 10248 |
| 20 and 197 | 3940 |
| 172 and 175 | 30100 |
| 43 and 68 | 2924 |