Least Common Multiple (LCM) of 172 and 146
The least common multiple (LCM) of 172 and 146 is 12556.
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 146?
First, calculate the GCD of 172 and 146 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 146 = 1 remainder 26 |
| 2 | 146 ÷ 26 = 5 remainder 16 |
| 3 | 26 ÷ 16 = 1 remainder 10 |
| 4 | 16 ÷ 10 = 1 remainder 6 |
| 5 | 10 ÷ 6 = 1 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 124 | 12524 |
| 12 and 108 | 108 |
| 63 and 120 | 2520 |
| 81 and 170 | 13770 |
| 149 and 32 | 4768 |