Least Common Multiple (LCM) of 115 and 78
The least common multiple (LCM) of 115 and 78 is 8970.
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 115 and 78?
First, calculate the GCD of 115 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 78 = 1 remainder 37 |
| 2 | 78 ÷ 37 = 2 remainder 4 |
| 3 | 37 ÷ 4 = 9 remainder 1 |
| 4 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 62 and 156 | 4836 |
| 31 and 140 | 4340 |
| 139 and 150 | 20850 |
| 50 and 12 | 300 |
| 97 and 66 | 6402 |