Least Common Multiple (LCM) of 134 and 157
The least common multiple (LCM) of 134 and 157 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 134 and 157?
First, calculate the GCD of 134 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 134 ÷ 157 = 0 remainder 134 |
| 2 | 157 ÷ 134 = 1 remainder 23 |
| 3 | 134 ÷ 23 = 5 remainder 19 |
| 4 | 23 ÷ 19 = 1 remainder 4 |
| 5 | 19 ÷ 4 = 4 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 87 and 115 | 10005 |
| 167 and 107 | 17869 |
| 191 and 139 | 26549 |
| 10 and 114 | 570 |
| 172 and 129 | 516 |