Least Common Multiple (LCM) of 200 and 21
The least common multiple (LCM) of 200 and 21 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 200 and 21?
First, calculate the GCD of 200 and 21 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 21 = 9 remainder 11 |
| 2 | 21 ÷ 11 = 1 remainder 10 |
| 3 | 11 ÷ 10 = 1 remainder 1 |
| 4 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 113 | 15594 |
| 117 and 149 | 17433 |
| 21 and 75 | 525 |
| 51 and 190 | 9690 |
| 199 and 147 | 29253 |