Least Common Multiple (LCM) of 146 and 172
The least common multiple (LCM) of 146 and 172 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 146 and 172?
First, calculate the GCD of 146 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 146 ÷ 172 = 0 remainder 146 |
| 2 | 172 ÷ 146 = 1 remainder 26 |
| 3 | 146 ÷ 26 = 5 remainder 16 |
| 4 | 26 ÷ 16 = 1 remainder 10 |
| 5 | 16 ÷ 10 = 1 remainder 6 |
| 6 | 10 ÷ 6 = 1 remainder 4 |
| 7 | 6 ÷ 4 = 1 remainder 2 |
| 8 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 11 and 192 | 2112 |
| 33 and 126 | 1386 |
| 136 and 24 | 408 |
| 170 and 151 | 25670 |
| 188 and 164 | 7708 |