Least Common Multiple (LCM) of 65 and 134
The least common multiple (LCM) of 65 and 134 is 8710.
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 65 and 134?
First, calculate the GCD of 65 and 134 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 134 = 0 remainder 65 |
| 2 | 134 ÷ 65 = 2 remainder 4 |
| 3 | 65 ÷ 4 = 16 remainder 1 |
| 4 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 63 | 3654 |
| 64 and 178 | 5696 |
| 112 and 17 | 1904 |
| 137 and 102 | 13974 |
| 105 and 21 | 105 |