Least Common Multiple (LCM) of 69 and 93
The least common multiple (LCM) of 69 and 93 is 2139.
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 93?
First, calculate the GCD of 69 and 93 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 93 = 0 remainder 69 |
| 2 | 93 ÷ 69 = 1 remainder 24 |
| 3 | 69 ÷ 24 = 2 remainder 21 |
| 4 | 24 ÷ 21 = 1 remainder 3 |
| 5 | 21 ÷ 3 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 75 | 525 |
| 97 and 55 | 5335 |
| 71 and 192 | 13632 |
| 70 and 180 | 1260 |
| 16 and 120 | 240 |