Least Common Multiple (LCM) of 157 and 134
The least common multiple (LCM) of 157 and 134 is 21038.
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 134?
First, calculate the GCD of 157 and 134 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 134 = 1 remainder 23 |
| 2 | 134 ÷ 23 = 5 remainder 19 |
| 3 | 23 ÷ 19 = 1 remainder 4 |
| 4 | 19 ÷ 4 = 4 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 165 | 9570 |
| 158 and 179 | 28282 |
| 32 and 33 | 1056 |
| 32 and 105 | 3360 |
| 108 and 194 | 10476 |