Least Common Multiple (LCM) of 76 and 117
The least common multiple (LCM) of 76 and 117 is 8892.
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 117?
First, calculate the GCD of 76 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 76 ÷ 117 = 0 remainder 76 |
| 2 | 117 ÷ 76 = 1 remainder 41 |
| 3 | 76 ÷ 41 = 1 remainder 35 |
| 4 | 41 ÷ 35 = 1 remainder 6 |
| 5 | 35 ÷ 6 = 5 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 74 | 4958 |
| 156 and 53 | 8268 |
| 89 and 70 | 6230 |
| 69 and 73 | 5037 |
| 31 and 22 | 682 |