Least Common Multiple (LCM) of 50 and 64
The least common multiple (LCM) of 50 and 64 is 1600.
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 64?
First, calculate the GCD of 50 and 64 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 50 ÷ 64 = 0 remainder 50 |
| 2 | 64 ÷ 50 = 1 remainder 14 |
| 3 | 50 ÷ 14 = 3 remainder 8 |
| 4 | 14 ÷ 8 = 1 remainder 6 |
| 5 | 8 ÷ 6 = 1 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 155 and 16 | 2480 |
| 125 and 80 | 2000 |
| 67 and 138 | 9246 |
| 132 and 46 | 3036 |
| 29 and 137 | 3973 |