Least Common Multiple (LCM) of 117 and 134
The least common multiple (LCM) of 117 and 134 is 15678.
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 117 and 134?
First, calculate the GCD of 117 and 134 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 134 = 0 remainder 117 |
| 2 | 134 ÷ 117 = 1 remainder 17 |
| 3 | 117 ÷ 17 = 6 remainder 15 |
| 4 | 17 ÷ 15 = 1 remainder 2 |
| 5 | 15 ÷ 2 = 7 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 33 | 3927 |
| 159 and 71 | 11289 |
| 147 and 55 | 8085 |
| 100 and 188 | 4700 |
| 114 and 183 | 6954 |