Least Common Multiple (LCM) of 172 and 123
The least common multiple (LCM) of 172 and 123 is 21156.
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 172 and 123?
First, calculate the GCD of 172 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 123 = 1 remainder 49 |
| 2 | 123 ÷ 49 = 2 remainder 25 |
| 3 | 49 ÷ 25 = 1 remainder 24 |
| 4 | 25 ÷ 24 = 1 remainder 1 |
| 5 | 24 ÷ 1 = 24 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 55 and 26 | 1430 |
| 37 and 98 | 3626 |
| 56 and 153 | 8568 |
| 43 and 177 | 7611 |
| 78 and 36 | 468 |