Least Common Multiple (LCM) of 120 and 200
The least common multiple (LCM) of 120 and 200 is 600.
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 120 and 200?
First, calculate the GCD of 120 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 200 = 0 remainder 120 |
| 2 | 200 ÷ 120 = 1 remainder 80 |
| 3 | 120 ÷ 80 = 1 remainder 40 |
| 4 | 80 ÷ 40 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 196 and 182 | 2548 |
| 121 and 103 | 12463 |
| 102 and 100 | 5100 |
| 78 and 72 | 936 |
| 70 and 157 | 10990 |