Least Common Multiple (LCM) of 200 and 69
The least common multiple (LCM) of 200 and 69 is 13800.
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 69?
First, calculate the GCD of 200 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 69 = 2 remainder 62 |
| 2 | 69 ÷ 62 = 1 remainder 7 |
| 3 | 62 ÷ 7 = 8 remainder 6 |
| 4 | 7 ÷ 6 = 1 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 74 and 121 | 8954 |
| 180 and 169 | 30420 |
| 156 and 128 | 4992 |
| 104 and 169 | 1352 |
| 28 and 64 | 448 |