Least Common Multiple (LCM) of 78 and 137
The least common multiple (LCM) of 78 and 137 is 10686.
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 137?
First, calculate the GCD of 78 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 137 = 0 remainder 78 |
| 2 | 137 ÷ 78 = 1 remainder 59 |
| 3 | 78 ÷ 59 = 1 remainder 19 |
| 4 | 59 ÷ 19 = 3 remainder 2 |
| 5 | 19 ÷ 2 = 9 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 153 | 19890 |
| 175 and 42 | 1050 |
| 109 and 56 | 6104 |
| 172 and 28 | 1204 |
| 135 and 155 | 4185 |