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 |
|---|---|
| 132 and 120 | 1320 |
| 155 and 84 | 13020 |
| 171 and 112 | 19152 |
| 74 and 110 | 4070 |
| 14 and 181 | 2534 |