Least Common Multiple (LCM) of 157 and 200
The least common multiple (LCM) of 157 and 200 is 31400.
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 157 and 200?
First, calculate the GCD of 157 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 200 = 0 remainder 157 |
| 2 | 200 ÷ 157 = 1 remainder 43 |
| 3 | 157 ÷ 43 = 3 remainder 28 |
| 4 | 43 ÷ 28 = 1 remainder 15 |
| 5 | 28 ÷ 15 = 1 remainder 13 |
| 6 | 15 ÷ 13 = 1 remainder 2 |
| 7 | 13 ÷ 2 = 6 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 78 | 4368 |
| 47 and 119 | 5593 |
| 28 and 77 | 308 |
| 88 and 34 | 1496 |
| 193 and 110 | 21230 |