Least Common Multiple (LCM) of 121 and 78
The least common multiple (LCM) of 121 and 78 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 121 and 78?
First, calculate the GCD of 121 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 121 ÷ 78 = 1 remainder 43 |
| 2 | 78 ÷ 43 = 1 remainder 35 |
| 3 | 43 ÷ 35 = 1 remainder 8 |
| 4 | 35 ÷ 8 = 4 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 25 and 83 | 2075 |
| 96 and 64 | 192 |
| 101 and 40 | 4040 |
| 105 and 162 | 5670 |
| 171 and 165 | 9405 |