Least Common Multiple (LCM) of 69 and 117
The least common multiple (LCM) of 69 and 117 is 2691.
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 69 and 117?
First, calculate the GCD of 69 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 117 = 0 remainder 69 |
| 2 | 117 ÷ 69 = 1 remainder 48 |
| 3 | 69 ÷ 48 = 1 remainder 21 |
| 4 | 48 ÷ 21 = 2 remainder 6 |
| 5 | 21 ÷ 6 = 3 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 55 and 84 | 4620 |
| 26 and 88 | 1144 |
| 185 and 188 | 34780 |
| 171 and 152 | 1368 |
| 85 and 145 | 2465 |