Least Common Multiple (LCM) of 78 and 125
The least common multiple (LCM) of 78 and 125 is 9750.
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 125?
First, calculate the GCD of 78 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 125 = 0 remainder 78 |
| 2 | 125 ÷ 78 = 1 remainder 47 |
| 3 | 78 ÷ 47 = 1 remainder 31 |
| 4 | 47 ÷ 31 = 1 remainder 16 |
| 5 | 31 ÷ 16 = 1 remainder 15 |
| 6 | 16 ÷ 15 = 1 remainder 1 |
| 7 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 139 and 89 | 12371 |
| 128 and 189 | 24192 |
| 115 and 45 | 1035 |
| 51 and 137 | 6987 |
| 117 and 23 | 2691 |