Least Common Multiple (LCM) of 21 and 200
The least common multiple (LCM) of 21 and 200 is 4200.
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 21 and 200?
First, calculate the GCD of 21 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 200 = 0 remainder 21 |
| 2 | 200 ÷ 21 = 9 remainder 11 |
| 3 | 21 ÷ 11 = 1 remainder 10 |
| 4 | 11 ÷ 10 = 1 remainder 1 |
| 5 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 190 and 70 | 1330 |
| 171 and 70 | 11970 |
| 101 and 150 | 15150 |
| 133 and 100 | 13300 |
| 124 and 21 | 2604 |