Least Common Multiple (LCM) of 200 and 113
The least common multiple (LCM) of 200 and 113 is 22600.
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 113?
First, calculate the GCD of 200 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 113 = 1 remainder 87 |
| 2 | 113 ÷ 87 = 1 remainder 26 |
| 3 | 87 ÷ 26 = 3 remainder 9 |
| 4 | 26 ÷ 9 = 2 remainder 8 |
| 5 | 9 ÷ 8 = 1 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 58 and 109 | 6322 |
| 75 and 138 | 3450 |
| 168 and 60 | 840 |
| 89 and 118 | 10502 |
| 165 and 11 | 165 |