Least Common Multiple (LCM) of 78 and 121
The least common multiple (LCM) of 78 and 121 is 9438.
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 121?
First, calculate the GCD of 78 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 121 = 0 remainder 78 |
| 2 | 121 ÷ 78 = 1 remainder 43 |
| 3 | 78 ÷ 43 = 1 remainder 35 |
| 4 | 43 ÷ 35 = 1 remainder 8 |
| 5 | 35 ÷ 8 = 4 remainder 3 |
| 6 | 8 ÷ 3 = 2 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 157 and 200 | 31400 |
| 110 and 102 | 5610 |
| 188 and 156 | 7332 |
| 31 and 174 | 5394 |
| 55 and 55 | 55 |