Least Common Multiple (LCM) of 50 and 85
The least common multiple (LCM) of 50 and 85 is 850.
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 85?
First, calculate the GCD of 50 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 50 ÷ 85 = 0 remainder 50 |
| 2 | 85 ÷ 50 = 1 remainder 35 |
| 3 | 50 ÷ 35 = 1 remainder 15 |
| 4 | 35 ÷ 15 = 2 remainder 5 |
| 5 | 15 ÷ 5 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 158 and 129 | 20382 |
| 63 and 42 | 126 |
| 174 and 108 | 3132 |
| 54 and 136 | 3672 |
| 40 and 19 | 760 |