Least Common Multiple (LCM) of 117 and 77
The least common multiple (LCM) of 117 and 77 is 9009.
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 117 and 77?
First, calculate the GCD of 117 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 77 = 1 remainder 40 |
| 2 | 77 ÷ 40 = 1 remainder 37 |
| 3 | 40 ÷ 37 = 1 remainder 3 |
| 4 | 37 ÷ 3 = 12 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 92 | 1840 |
| 54 and 96 | 864 |
| 102 and 61 | 6222 |
| 22 and 134 | 1474 |
| 82 and 189 | 15498 |