Least Common Multiple (LCM) of 87 and 50
The least common multiple (LCM) of 87 and 50 is 4350.
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 87 and 50?
First, calculate the GCD of 87 and 50 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 87 ÷ 50 = 1 remainder 37 |
| 2 | 50 ÷ 37 = 1 remainder 13 |
| 3 | 37 ÷ 13 = 2 remainder 11 |
| 4 | 13 ÷ 11 = 1 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 152 and 148 | 5624 |
| 122 and 37 | 4514 |
| 19 and 91 | 1729 |
| 185 and 138 | 25530 |
| 200 and 22 | 2200 |