Least Common Multiple (LCM) of 50 and 65
The least common multiple (LCM) of 50 and 65 is 650.
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 50 and 65?
First, calculate the GCD of 50 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 50 ÷ 65 = 0 remainder 50 |
| 2 | 65 ÷ 50 = 1 remainder 15 |
| 3 | 50 ÷ 15 = 3 remainder 5 |
| 4 | 15 ÷ 5 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 107 | 13161 |
| 82 and 132 | 5412 |
| 76 and 147 | 11172 |
| 182 and 62 | 5642 |
| 55 and 80 | 880 |