Least Common Multiple (LCM) of 69 and 172
The least common multiple (LCM) of 69 and 172 is 11868.
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 172?
First, calculate the GCD of 69 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 172 = 0 remainder 69 |
| 2 | 172 ÷ 69 = 2 remainder 34 |
| 3 | 69 ÷ 34 = 2 remainder 1 |
| 4 | 34 ÷ 1 = 34 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 177 and 100 | 17700 |
| 89 and 77 | 6853 |
| 122 and 93 | 11346 |
| 64 and 82 | 2624 |
| 96 and 125 | 12000 |