Least Common Multiple (LCM) of 200 and 26
The least common multiple (LCM) of 200 and 26 is 2600.
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 200 and 26?
First, calculate the GCD of 200 and 26 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 26 = 7 remainder 18 |
| 2 | 26 ÷ 18 = 1 remainder 8 |
| 3 | 18 ÷ 8 = 2 remainder 2 |
| 4 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 175 | 4200 |
| 24 and 105 | 840 |
| 77 and 46 | 3542 |
| 114 and 182 | 10374 |
| 99 and 120 | 3960 |