Least Common Multiple (LCM) of 78 and 134
The least common multiple (LCM) of 78 and 134 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 78 and 134?
First, calculate the GCD of 78 and 134 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 134 = 0 remainder 78 |
| 2 | 134 ÷ 78 = 1 remainder 56 |
| 3 | 78 ÷ 56 = 1 remainder 22 |
| 4 | 56 ÷ 22 = 2 remainder 12 |
| 5 | 22 ÷ 12 = 1 remainder 10 |
| 6 | 12 ÷ 10 = 1 remainder 2 |
| 7 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 43 | 1333 |
| 65 and 155 | 2015 |
| 118 and 95 | 11210 |
| 55 and 111 | 6105 |
| 108 and 122 | 6588 |