Least Common Multiple (LCM) of 78 and 157
The least common multiple (LCM) of 78 and 157 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 78 and 157?
First, calculate the GCD of 78 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 157 = 0 remainder 78 |
| 2 | 157 ÷ 78 = 2 remainder 1 |
| 3 | 78 ÷ 1 = 78 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 158 and 116 | 9164 |
| 147 and 18 | 882 |
| 71 and 44 | 3124 |
| 88 and 198 | 792 |
| 16 and 67 | 1072 |