Least Common Multiple (LCM) of 157 and 20
The least common multiple (LCM) of 157 and 20 is 3140.
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 20?
First, calculate the GCD of 157 and 20 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 20 = 7 remainder 17 |
| 2 | 20 ÷ 17 = 1 remainder 3 |
| 3 | 17 ÷ 3 = 5 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 164 and 156 | 6396 |
| 54 and 54 | 54 |
| 24 and 159 | 1272 |
| 175 and 190 | 6650 |
| 152 and 71 | 10792 |