Least Common Multiple (LCM) of 36 and 134
The least common multiple (LCM) of 36 and 134 is 2412.
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 36 and 134?
First, calculate the GCD of 36 and 134 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 36 ÷ 134 = 0 remainder 36 |
| 2 | 134 ÷ 36 = 3 remainder 26 |
| 3 | 36 ÷ 26 = 1 remainder 10 |
| 4 | 26 ÷ 10 = 2 remainder 6 |
| 5 | 10 ÷ 6 = 1 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 86 and 147 | 12642 |
| 128 and 171 | 21888 |
| 13 and 127 | 1651 |
| 51 and 110 | 5610 |
| 189 and 85 | 16065 |