Least Common Multiple (LCM) of 200 and 51
The least common multiple (LCM) of 200 and 51 is 10200.
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 51?
First, calculate the GCD of 200 and 51 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 51 = 3 remainder 47 |
| 2 | 51 ÷ 47 = 1 remainder 4 |
| 3 | 47 ÷ 4 = 11 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 139 | 22935 |
| 151 and 145 | 21895 |
| 181 and 66 | 11946 |
| 121 and 99 | 1089 |
| 85 and 119 | 595 |