Least Common Multiple (LCM) of 137 and 200
The least common multiple (LCM) of 137 and 200 is 27400.
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 137 and 200?
First, calculate the GCD of 137 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 200 = 0 remainder 137 |
| 2 | 200 ÷ 137 = 1 remainder 63 |
| 3 | 137 ÷ 63 = 2 remainder 11 |
| 4 | 63 ÷ 11 = 5 remainder 8 |
| 5 | 11 ÷ 8 = 1 remainder 3 |
| 6 | 8 ÷ 3 = 2 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 38 and 101 | 3838 |
| 25 and 77 | 1925 |
| 167 and 74 | 12358 |
| 31 and 178 | 5518 |
| 129 and 129 | 129 |