Least Common Multiple (LCM) of 157 and 100
The least common multiple (LCM) of 157 and 100 is 15700.
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 100?
First, calculate the GCD of 157 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 100 = 1 remainder 57 |
| 2 | 100 ÷ 57 = 1 remainder 43 |
| 3 | 57 ÷ 43 = 1 remainder 14 |
| 4 | 43 ÷ 14 = 3 remainder 1 |
| 5 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 65 | 7345 |
| 109 and 174 | 18966 |
| 127 and 51 | 6477 |
| 63 and 199 | 12537 |
| 39 and 39 | 39 |