Least Common Multiple (LCM) of 157 and 75
The least common multiple (LCM) of 157 and 75 is 11775.
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 75?
First, calculate the GCD of 157 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 75 = 2 remainder 7 |
| 2 | 75 ÷ 7 = 10 remainder 5 |
| 3 | 7 ÷ 5 = 1 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 35 | 175 |
| 11 and 150 | 1650 |
| 197 and 137 | 26989 |
| 200 and 148 | 7400 |
| 17 and 185 | 3145 |