Least Common Multiple (LCM) of 134 and 78
The least common multiple (LCM) of 134 and 78 is 5226.
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 78?
First, calculate the GCD of 134 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 134 ÷ 78 = 1 remainder 56 |
| 2 | 78 ÷ 56 = 1 remainder 22 |
| 3 | 56 ÷ 22 = 2 remainder 12 |
| 4 | 22 ÷ 12 = 1 remainder 10 |
| 5 | 12 ÷ 10 = 1 remainder 2 |
| 6 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 24 and 66 | 264 |
| 13 and 173 | 2249 |
| 43 and 123 | 5289 |
| 115 and 61 | 7015 |
| 140 and 129 | 18060 |