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 |
|---|---|
| 83 and 161 | 13363 |
| 173 and 188 | 32524 |
| 65 and 56 | 3640 |
| 47 and 148 | 6956 |
| 155 and 167 | 25885 |