Least Common Multiple (LCM) of 102 and 200
The least common multiple (LCM) of 102 and 200 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 102 and 200?
First, calculate the GCD of 102 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 200 = 0 remainder 102 |
| 2 | 200 ÷ 102 = 1 remainder 98 |
| 3 | 102 ÷ 98 = 1 remainder 4 |
| 4 | 98 ÷ 4 = 24 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 72 and 92 | 1656 |
| 137 and 112 | 15344 |
| 159 and 178 | 28302 |
| 88 and 191 | 16808 |
| 175 and 143 | 25025 |