Least Common Multiple (LCM) of 157 and 78
The least common multiple (LCM) of 157 and 78 is 12246.
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 157 and 78?
First, calculate the GCD of 157 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 78 = 2 remainder 1 |
| 2 | 78 ÷ 1 = 78 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 71 | 9159 |
| 190 and 163 | 30970 |
| 54 and 118 | 3186 |
| 103 and 21 | 2163 |
| 188 and 74 | 6956 |