Least Common Multiple (LCM) of 76 and 121
The least common multiple (LCM) of 76 and 121 is 9196.
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 76 and 121?
First, calculate the GCD of 76 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 76 ÷ 121 = 0 remainder 76 |
| 2 | 121 ÷ 76 = 1 remainder 45 |
| 3 | 76 ÷ 45 = 1 remainder 31 |
| 4 | 45 ÷ 31 = 1 remainder 14 |
| 5 | 31 ÷ 14 = 2 remainder 3 |
| 6 | 14 ÷ 3 = 4 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 194 and 121 | 23474 |
| 25 and 163 | 4075 |
| 144 and 112 | 1008 |
| 181 and 47 | 8507 |
| 129 and 112 | 14448 |