Least Common Multiple (LCM) of 84 and 200
The least common multiple (LCM) of 84 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 84 and 200?
First, calculate the GCD of 84 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 200 = 0 remainder 84 |
| 2 | 200 ÷ 84 = 2 remainder 32 |
| 3 | 84 ÷ 32 = 2 remainder 20 |
| 4 | 32 ÷ 20 = 1 remainder 12 |
| 5 | 20 ÷ 12 = 1 remainder 8 |
| 6 | 12 ÷ 8 = 1 remainder 4 |
| 7 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 156 | 780 |
| 21 and 77 | 231 |
| 64 and 135 | 8640 |
| 75 and 181 | 13575 |
| 63 and 145 | 9135 |